Pakistan said on Thursday three of its soldiers were killed in a cross-border exchange of fire in the contested Kashmir region, but India denied that five of its troops died, too.

Major-General Asif Ghafoor, a spokesman for the Pakistan armed forces, said its three soldiers had died along with five of India's when Indian forces opened fire along the contested border known as the line of control.

"Intermittent exchange of fire continues," Ghafoor said.

An Indian army spokesman denied that. "No casualties. This assertion is wrong," the spokesman said. In a statement, the Indian army said that from around 7 a.m. local time, Pakistan violated a ceasefire between the two countries.

The flare-up comes at a time of heightened tensions between India and Pakistan, both of which administer portions of Kashmir while claiming all of it. India's Hindu nationalist government revoked the special status of the portion of Muslim-majority Kashmir it controls on Aug. 5.

Indian Prime Minister Narendra Modi said in a speech Thursday marking India Independence Day that stripping the disputed Kashmir region of its statehood and special constitutional provisions has helped unify the country.

Modi spoke from India's Mughal-era Red Fort in New Delhi as an unprecedented security lockdown kept people in Indian-administered Kashmir indoors for an 11th day.

'The old arrangement in Jammu, Kashmir and Ladakh encouraged corruption,' Indian Prime Minister Narendra Modi said during an Independence Day address. (Prakash Singh/AFP/Getty Images)

In his live address, Modi said the region's previous status — some political autonomy and a ban on outsiders buying land and taking public sector jobs in the Muslim-majority Himalayan region — had fuelled a movement for separatism and was unjust for Kashmiri women, because the law said that they lost their inheritance rights if marrying a person from outside the region.

"The old arrangement in Jammu, Kashmir and Ladakh encouraged corruption, nepotism but there was injustice when it came to rights of women, children, Dalits, tribal communities," Modi said in the speech marking 72 years since India achieved independence from British rule.

A lockdown in Indian-administered Kashmir has been in place since Aug. 4, just before a presidential order to subsume the Muslim-majority region into India's federal government by revoking Article 370 of the constitution and downgrading the state of Jammu and Kashmir into two union territories. A new law allows anyone to buy land there, which some Kashmiris fear could change the region's culture and demographics.

An Indian paramilitary soldier stands guard on a deserted road leading towards an Independence Day parade venue during lockdown in the city of Srinagar in Indian-administered Kashmir. (Dar Yasin/Associated Press)

India's Foreign Ministry officials have said Kashmir is returning to normalcy, but The Associated Press and other news organizations operating in the region describe the severe constraints, including the suspension of internet, cellphone and landline services and steel and barbed-wire street blockades.

While daily protests have erupted in Kashmir, Modi has received widespread public support in other parts of India.

"Article 370 should have been removed a long time ago, but better late than never," Amarjeet Singh, a businessman from New Delhi, said outside the Red Fort as India finalized preparations on Wednesday.

"It is good. Everyone will be benefited by this, because every common man will be able to work there and start business there," Singh said.

On Thursday, turning to his agenda to make India a $5-trillion US economy in the next five years, Modi said that the changes in Kashmir will help the region contribute more to India's development.

"In the last 70 years we became a $2 trillion [US] economy, but in the last five years, we added $1 trillion to the economy. This gives me the confidence of becoming a $5-trillion [US] economy in the coming years," Modi said.

The prime minister, whose Hindu nationalist Bharatiya Janata Party won a landslide victory in general elections in May, also announced the creation of a new chief of defence staff to co-ordinate the country's security operations.

He also made a pitch for restructuring India's electoral system so that state and lower house of parliament elections are held simultaneously rather than on separate timetables.