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Mr Modi said India-administered Kashmir would play an "important role" in his country's future Indian PM Narendra Modi has said his decision to strip Indian-administered Kashmir of its special status will restore the region to its "past glory".
Pakistan's PM Imran Khan earlier criticised India's move, warning "the world's eye is on Kashmir".
Both leaders covered the tense situation in Kashmir in their independence day speeches, a day apart.The disputed territory has been the site of decades of sporadic conflict and is now in lockdown.
Kashmir: A priority for British Asians?A communications blackout in the region has made reporting from India-administered Kashmir difficult - but Mr Modi did not mention the restrictions in his speech.
India celebrates Independence Day one day after Pakistan.
The two separate states came into existence as a result of the partition of British India in 1947.
Media captionTwo wars, a 60-year dispute - a history of the Kashmir conflictWhat did the leaders say?Mr Modi criticised people at home who opposed the revocation of Article 370, accusing them of "playing politics", and said Kashmir will play an "important role" in India's development.
He said Article 370, the constitutional provision that granted it special status, had only encouraged corruption.
Viewpoint: Why Modi's Kashmir move is widely supportedViewpoint: Has India pushed Kashmir to a point of no return?What happened in Kashmir and why it mattersMr Khan, meanwhile, used his speech to issue a warning: "Whatever was done during the curfew by India, we will tell the international community that you are responsible."
"Whichever forum we get, I will be the ambassador and bring up Kashmir at every forum," he said.
Image copyrightAFPImage captionImran Khan pledged to champion the Kashmir issue on the international stageMany Kashmiris believe that Mr Modi's Hindu nationalist government's move is aimed at changing the demographics of the region by allowing other Indians to permanently settle there.
The government denies this and has consistently framed its move as one made to facilitate economic development and security.
Mr Modi said past governments had lacked the courage to take such a bold step because they were worried about their political future.
"I don't care about my political future.
For me, the country's future comes first."
What else is happening in Kashmir?Kashmir has been in lockdown for more than a week now, with mobile, landline and internet networks cut off and curfew-like restrictions that ban people from assembling in crowds.
However, officials said on Wednesday that these restrictions had now been eased in the Hindu-majority Jammu region.
The BBC World Service, meanwhile, has stepped up its output on shortwave radio in Indian-administered Kashmir amid the communications shutdown.
Broadcasts in English, Urdu, Hindi, Dari, and Pashto languages are available in the region, the BBC said.
The Line of Control - the de facto border which marks the division of the parts of Kashmir administered by India and Pakistan - was the site of at least eight deaths, Pakistani officials said.
Three soldiers died in Indian shelling across the Line of Control but return fire killed five on the Indian side, they said.
Indian officials did not confirm those deaths, and Indian news agency ANI said Indian army officials had denied the claim - labelling the exchange of fire as "ceasefire violations" by Pakistan.
Fire continues to be exchanged intermittently, Pakistan's armed forces said.
Despite the security clampdown however, there have been protests against the revocation of Article 370, including one last Friday in Srinagar in the Muslim-majority Kashmir valley.
It involved thousands of people coming out after midday prayers to demonstrate against the move.
Thousands gathered in London outside the Indian High Commission to protest against the scrapping of Kashmir's special status on Thursday.
Media captionThe Indian government has said this protest never took placeAlthough Kashmir took centre stage during Mr Modi's Independence Day speech, the Indian prime minister also made several other important announcements.
For the first time in the history of independent India, there will be a Chief of Defence Staff who will have authority over all three of India's armed forces.
'Even I will pick up a gun': Inside Kashmir's lockdownThe Indians celebrating Kashmir's loss of autonomyHe also addressed the problem of single-use plastic items, urging people to reduce their usage, and referred to other issues such as water shortages, population control and healthcare.
nside Kashmir's lockdownKashmiris say they are living in an "open-air prison"Indian-administered Kashmir has been under an unprecedented lockdown since Monday, when India revoked a special constitutional status dating back nearly 70 years.
The BBC's Geeta Pandey travelled for two days around the region, where a bitter sense of betrayal threatens to fuel fresh conflict.
In the heart of Srinagar city, Khanyar is an area notorious for anti-India protests.
To get here during what amounts to a virtual 24-hour curfew, we pass through half a dozen roadblocks.As we come across yet another barricade, I get out of my car to take some photos.
A few men emerge from a laneway to complain about living under what to many feels like a siege.
"This is extreme thuggery on the government's part," says an elderly member of the group.
The paramilitary police try to hustle us away but the man wants to be heard.
"You lock us up during the day.
You lock us up at night," he shouts angrily, wagging his finger.
The policeman says there's a curfew in place and that they must go inside immediately.
But the diminutive old man stands his ground and challenges him again.
At that point, I'm ordered to leave.
But before I can, a young man, carrying his toddler son in his arms, tells me he is ready to pick up a gun to fight India.
"This is my only son.
He's too small now, but I will prepare him to pick up a gun too," he says.
He's so angry that he doesn't even care that he's saying all this within earshot of the policeman standing near us.
Media captionYoung Kashmiris on India's decision: "We've been pushed back into medieval times"Across the Muslim-majority Kashmir valley, I meet men who tell me they no longer want to live life in fear of the security forces.
An insurgency has been taking place here for 30 years, but what residents call a "dictatorial order" from far-away Delhi has pushed people who never supported separatism into a corner.
They say it will have serious consequences for both Kashmir and India.
This is very much the dominant sentiment everywhere I go - anger mixed with fear and worry, and a fierce determination to resist the central government's move.
Srinagar - the summer capital of Jammu and Kashmir - has been under a virtual lockdown since Monday morning and the city resembles a ghost town.
Shops, schools, colleges and offices are all shut and there is no public transport on the roads.
What happened in Kashmir and why it mattersWhy India and Pakistan fight over KashmirThousands of gun-wielding troops patrol deserted streets that are barricaded with coils of razor wire, and residents remain locked up inside their homes.
For nearly a week now, two of the former state chief ministers have been in detention while a third, who is currently an MP from the state, is under house arrest.
Hundreds of others, including activists, business leaders and professors, have also been detained and are being held in makeshift prisons.
Rizwan Malik says Kashmir "now feels like a jail, a big open-air jail".
He flew from Delhi to Srinagar less than 48 hours after Home Minister Amit Shah laid out his plans for Kashmir in the parliament on Monday.
Image copyrightABID BHATImage captionRizwan Malik flew from Delhi to Srinagar because he couldn't reach his parents on the phone for two daysHe said he had last spoken to his parents on Sunday night, a few hours before the government shut down all communications, including the internet.
There was a total information blackout, and because he couldn't reach any of his friends or relatives either, he decided to return home.
"It's the first time in my life that we had no way of communicating with anyone.
Never before have I seen anything like this," he told me at his parents' home in Srinagar.
Mr Malik is furious that India has revoked Kashmir's special status - which gave it a significant degree of autonomy and underpinned the region's relationship with the rest of India for decades - without consulting the state's people.
He's not someone who believes in separatism, or has ever gone out and thrown stones at soldiers in protest; he's a 25-year-old aspirational young man studying to be an accountant in Delhi.
He says he has long believed in the idea of India because he is sold on the story of its economic success.
"If India wants us to believe that it's a democracy, they are fooling themselves.
Kashmir has long had an uneasy relationship with India [but] our special status was the bridge that joined the two.
By scrapping it, they have taken away our identity.
This is unacceptable to any Kashmiri," he says.
Image copyrightABID BHATImage captionThousands of troops are on patrol in SrinagarWhen the siege is lifted and protesters are able to take to the streets, Mr Malik predicts that every Kashmiri will join them: "It was said that in every family one brother is with the separatists and the other is with the [Indian] mainstream.
Now the Indian government has united the two."
His sister Rukhsar Rashid, a 20-year-old architecture student at Kashmir University, says when she heard the home minister's speech on TV, her hands began to shake and her mother, sitting next to her, began to cry.
"She was saying death would be better than this," says Ms Rashid.
"I keep waking up with panic attacks.
My grandparents who live in the city's Batmaloo area say it has turned into Afghanistan."
India had been building up to its big move on the part of Kashmir it controls for some time.
The government first announced late last month it was sending more than 35,000 additional troops to the region, an area that's already the most militarised in the world because it is disputed between nuclear-armed India and Pakistan.
Image copyrightABID BHATImage captionRoads across Srinagar are barricaded with concertina wiresLast week, the annual Hindu pilgrimage to the Amarnath cave shrine was called off abruptly as the authorities warned of a terror threat.
Then, hotels and houseboats along the picturesque Dal Lake were ordered shut and tourists asked to leave.
Everyone in Kashmir by then knew something was afoot, but of the dozens of people I spoke to, no-one expected Delhi would go this far and unilaterally revoke part of the constitution.
The communications blackout means reliable information is hard to come by, and news of what's going on spreads by word of mouth.
Despite the lockdown, we hear daily reports of protesters pelting security forces with stones in Srinagar and elsewhere.
We hear a protester drowned when he was chased by troops and jumped in a river.
Several people are believed to be injured and in hospital.
But the Indian government has been trying to show that all's well in Kashmir.
'India has betrayed Kashmir'Modi defends lifting Kashmir's special statusThe Indians celebrating Kashmir's loss of autonomyOn Wednesday, TV channels showed National Security Advisor Ajit Doval lunching with a group of men on the streets of Shopian, a town that's described in the Indian press as "a hotbed of militancy".
It was an attempt to tell the world that there's popular support for the government's move even in the most difficult of areas and that peace and calm prevails.
But Kashmiris have dismissed it as a stunt.
"If people are happy, then why do they need the curfew? Why is there a communication shutdown?" asks Rizwan Malik.
The same question is repeated in every part of Srinagar - in homes, on the streets, in the sensitive old city areas that the locals call "downtown", and in the southern district of Pulwama, home to the militant who carried out the audacious suicide bombing targeting the security forces in February that brought India and Pakistan close to war.
Media captionThe BBC reports from inside Indian-administered KashmirAs I drive through the region, men hanging out in groups by the roadside or in moving vehicles flag down my car to talk to me.
They say Kashmiri voices are being suppressed, and they are desperate to be heard.
They tell me how angry they are and issue dire warnings of impending bloodshed.
"Kashmir is under siege at the moment.
The moment it's lifted, trouble will start," says Zahid Hussain Dar, a lawyer living in Pulwama.
"Once the political and separatist leaders are freed from detention or house arrest, there will be calls for protests and people will come out."
Tracing the path that led to the Pulwama attackThe funerals driving Kashmiri youth to militancyShock and concern in locked-down KashmirSome in the Indian press have reported that since there have been no major protests in Kashmir valley so far, it means people have accepted the government's decision.
But the Kashmir I see is seething.
I've been visiting the region regularly for over 20 years to report on the long-running insurgency against Indian rule, but the sort of anger and resentment that is being expressed now is unprecedented.
Image copyrightABID BHATImage captionThe government ordered tourists to leave Kashmir ahead of the lockdownMost people here say they will settle for nothing less than the government rescinding its order and restoring Kashmir's special status.
But Prime Minister Narendra Modi's government is not known for rolling back decisions and this underpins fears in the valley that the government will come down heavily on those who resist.
Image copyrightABID BHATImage captionMuskaan Lateef says tensions in Kashmir could boil overOn Thursday, Mr Modi defended his controversial decision, saying it was "the beginning of a new era" and promising employment opportunities and development for Kashmir.
Yet not many here are ready to back down.
And it does not augur well for either Kashmiris or India.
Muskaan Lateef, a high school student, describes the current situation as "the calm before the storm".
"It's like the oceans are quiet, but the tsunami is about to hit the shore."
