The leaders of India and Pakistan have pledged to restore calm on their disputed border in Kashmir, with New Delhi demanding action before any improvement in relations.

Pakistani Prime Minister Nawaz Sharif, who has advocated an end to historic tensions with India since sweeping to power in the May elections, held his first meeting with his counterpart Manmohan Singh on the sidelines of the annual UN summit on Sunday.

An Indian official said the two leaders, who met for more than an hour in a New York hotel, decided to task senior military officers to "find effective means to restore the cease-fire" 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 Line of Control," Indian national security adviser Shivshankar Menon told reporters, referring to the line that demarcates the boundary between India- and Pakistan-controlled parts of Kashmir.

Earlier this year, Pakistani and Indian troops were involved in some of their worst skirmishes in a decade in Kashmir, which is claimed in full by both nuclear-armed rivals. And three days before the New York talks, militants raided an army base on the Indian side of Kashmir, killing 10 people.

India accuses Pakistan of sponsoring militants, but violence has subsided sharply since the two countries entered a cease-fire in 2003.

Pakistani Foreign Secretary Jalil Abbas Jilani confirmed that the two prime ministers agreed that the ceasefire "should be respected in letter and spirit". But he played down India's warnings that the relationship hinged on calm in Kashmir, calling the meeting "extremely positive", and saying Sharif was committed to a "peaceful and sustained dialogue" with India.

Sharif, who was elected on promises to revive Pakistan's troubled economy, has moved quickly to ease concerns in India. In a speech before the UN General Assembly on Friday, Sharif called for a "new beginning" with India, saying the two developing nations had wasted money in their intense military buildup over the decades.

But India has been pressing for concrete action by Pakistan since the sensational 2008 assault on Mumbai, in which Islamic militants laid siege to an iconic hotel, apart from attacking other places, killing 166 people.