NEW DELHI, Aug 15 (Reuters) - India's prime minister, using his strongest language against Pakistan since the two countries pulled back from the brink of war in June, accused Islamabad on Thursday of "cross-border terrorism" in disputed Kashmir.

Atal Behari Vajpayee's speech appeared to be in response to an address by Pakistan President Pervez Musharraf who said India's plans to hold elections in Jammu and Kashmir state in September and October were farcical.

Both countries were marking 55 years of independence from British rule -- Pakistan on Wednesday and India on Thursday -- when the subcontinent was divided into Islamic Pakistan and mostly Hindu but secular India.

"Our neighbour claims to be fighting terrorism in international forum. But in this region it has double standards," Vajpayee said. "It is trying to get Jammu and Kashmir through cross-border terrorism," he added.

India has long accused Pakistan of "cross-border terrorism" by helping Islamic militants infiltrate into Jammu and Kashmir, India's only Muslim-majority state, to join a 13-year revolt against Indian rule.

The nuclear rivals came to the brink of war over the dispute in June in a crisis eased only after Musharraf, under intense U.S. pressure, promised Washington he would permanently end infiltration into Indian Kashmir.

Vajpayee said infiltration into Kashmir was continuing and accused Pakistan of interfering in the state elections by effectively calling for a boycott.

India sees Kashmir as an integral part of the country and is determined to hold state elections as a means of bringing peace to the region and showing the legitimacy of its rule there.

INSULTS TRADED OVER ELECTIONS

Musharraf said on Wednesday Pakistan could not be blamed for Kashmiri separatist violence, saying India's poll plans were an effort to give legitimacy to its "illegal occupation" of Kashmir.

"The government of India has organised such farcical elections in the past," he said.

"These so-called elections have invariably been rigged and have always been boycotted by the Kashmiri people."

Kashmiri separatist groups have said they will not participate in the elections, to be held in four rounds starting on September 16, with counting due on October 10.

Vajpayee in turn said Musharraf, who seized power in a military coup in 1999, had no right to preach about democracy.

"Those calling forthcoming elections in Jammu and Kashmir as a farce should not give us lessons in democracy," he said, speaking at the 17th century Red Fort, built by India's former Islamic Moghul rulers.

"They should look inside themselves. How can there be an atmosphere for meaningful talks if the people of Jammu and Kashmir are openly being asked to boycott the elections?"

Islamabad says the Kashmiri people should be allowed a plebiscite to decide whether to join India or Pakistan, in line with United Nations resolutions in 1948 and 1949.

But India, which fears other states could try to secede if it lost Kashmir, says Pakistan effectively renounced the U.N. resolutions in a subsequent peace treaty in which both sides agreed to resolve the Kashmir dispute bilaterally.

PAST MISTAKES

While taking a hard line on Pakistan, Vajpayee was conciliatory to Kashmiri people, offering them more autonomy after the elections which India says will be free and fair.

"I want to assure the people of Jammu and Kashmir that if there have been mistakes, we will correct them. For this we will talk to elected representatives and organisations. There will be discussion on the demand to give greater powers to the state."

But his comments fell short of demands by separatists who want talks as a prelude to holding elections, and some say the poll should be held under the auspices of the state governor, rather than under the ruling National Conference, a pro-Delhi Kashmiri party who they accuse of rigging elections in the past.

India and Pakistan have fought two of their three wars since independence over Kashmir, and mobilised close to a million men on their border after a December attack on India's parliament, blamed by New Delhi on Pakistan-based Kashmiri separatists.

Reflecting fears of fresh militant attacks, India stepped up security across the country for Independence Day.

Helicopters hovered overhead as Vajpayee made his speech behind bullet-proof glass, cars in the capital were stopped and searched, police commandos armed with machine-guns lined the streets and many mobile phones were jammed. Nampa-Reuters 0647 150802 WEB story ENDS (NAMPA 150651)