The leaders of India and Pakistan have pledged to find ways to restore calm on their border in Kashmir as an initial step towards reconciliation, according to an Indian official.
Nawaz Sharif, Pakistani prime minister, has advocated an end to tensions with India since he came to power in May elections.
He held his first meeting with his Indian counterpart, Manmohan Singh, on Sunday on the sidelines of the annual UN General Assembly summit.
An Indian official said that the two leaders, who met for more than an hour in a New York hotel, decided to entrust senior military officers with the task of finding "effective means to restore the ceasefire" in divided Kashmir.
"Both agreed that the precondition for forward movement in the relationship, which they both desire, is really an improvement of the situation on the LoC," Shivshankar Menon, Indian national security adviser, said, referring to the Line of Control in the Himalayan territory.
The talks come after fighters raided an army base on the Indian side of Kashmir on Thursday, killing 10 people in an attack seen as aimed at holding back reconciliation efforts between the neighbours.
The clashes in Kashmir have killed at least eight soldiers from both countries in less than two months.
Mumbai attack factor
Fighters linked to Pakistan carried out a coordinated attack in 2008 in the Indian metropolis of Mumbai, killing 166 people and laying siege to a famous hotel among other places.
Menon said that Sharif promised "there would be action" on punishing fighters over the Mumbai attack, and said the talks were friendly.
But he added: "As for how useful and productive the meeting was, I think the only proof will be in the months to come."
Sharif and Singh extended invitations to visit the other country, but no dates were set, Menon said.
Sharif, in a speech to the UN General Assembly, on Friday called for a "new beginning" with India and denounced the developing nations' years of intense military development as a waste of resources.
But Singh, who did not speak publicly on Sunday, has said that Pakistan must stop being "the epicentre of terrorism" in South Asia.
"For progress to be made, it is imperative that the territory of Pakistan and the areas under its control are not utilised for aiding or abetting terrorism," Singh said from the UN podium on Saturday.
"It is equally important that the terrorist machinery that draws its sustenance from Pakistan be shut down," he said.
Singh resisted domestic pressure for military retaliation after the Mumbai attack five years ago.
He instead pressed Pakistan to prosecute the group Lashkar-e-Taiba and has said he has been disappointed by Pakistan's response.
Sharif, who earlier in his career maintained relations with Pakistani religious groups, has tried to reassure India after his election as he puts a top priority on reviving Pakistan's troubled economy.
After his election, Pakistan freed nearly 340 Indian fishermen in a goodwill gesture and Sharif called for greater economic cooperation with the larger neighbour.
Sharif was prime minister during the Kargil conflict in 1999 when Pakistan-linked forces infiltrated remote Himalayan terrain on the Indian side of Kashmir, just months after Atal Bihari Vajpayee, India's then prime minister, travelled across the border with high hopes of reconciliation.
The South Asia Terrorism Portal, which tracks the violence in Kashmir, says this year's toll is 44 members of the security forces, up from 17 for all of last year.
India accuses Pakistan of sponsoring the fighters, though the violence has subsided sharply since the 1990s and early 2000s.