The leaders of India and Pakistan have pledged to work together to halt a recent upsurge of violence in Kashmir, according to senior officials.
Both sides were upbeat about the pair's first meeting since the May election of Pakistan Prime Minister Nawaz Sharif.
On Saturday, India's Manmohan Singh told the UN General Assembly Pakistan had to stop being "the epicentre of terrorism".
Bilateral ties have been strained over deadly clashes in the disputed region.
On Thursday, at least 10 people were killed when militants stormed a police station and an army camp in Indian-administered Kashmir.
Delhi has also blamed Pakistan-based militants for the deadly attacks in Mumbai in 2008, urging Islamabad to punish the perpetrators.
The two leaders met for over an hour on the sidelines of the UN assembly in New York, for talks described by Pakistan's Foreign Secretary Jalil Abbas Jilani as "extremely positive".
"They were both agreed that the pre-conditions for forward movement in the relationship which they both desire is an improvement of the situation on the Line of Control where there have been repeated ceasefire violations," Indian national security adviser Shivshankar Menon told reporters.
Kashmir is divided between India and Pakistan by the Line of Control (LoC).
"Our overall impression of the meeting was that it was useful because it provided an opportunity for high-level contact on issues that are troubling the relationship,'' he said.
"We will now see how both sides take it forward in the next few months."
Mr Jilani said both leaders had committed themselves to "better relations between the two countries" and agreed the ceasefire should be respected "in letter and spirit".
The two men agreed to pay visits to each other's respective countries, Mr Menon said, though no dates were set.
India has long accused Pakistan of sponsoring militants in the disputed region - though despite a recent spike, overall the violence has declined since the early 2000s.
But relations plunged again over the 2008 Mumbai attack.
Mr Singh, 81, has expressed disappointment in the Pakistani response and reiterated a call for Pakistan to rein in militants in his UN speech.
Mr Sharif swept to power in May with pledges to improve ties with India.