Addressing media after the ice-breaking "useful and friendly" talks here Sunday on the sidelines of the UN general assembly, Indian National Security Advisor Shivshankar Menon said Manmohan Singh told Sharif that it was vital to bring to book those in Pakistan who masterminded the Mumbai terror attack that killed 166 people including many foreigners.
According to Menon, Sharif said that indeed was Pakistan's intention.
"Both sides wish to see a better India-Pakistan relationship. Both sides want a much better relationship," Menon told media.
"In order to get there, we need to address today the issues we face," he added, which he said included restoring "peace and tranquillity" along the LoC and addressing issues related to terrorism.
"It is very important to address the terrorism issue," Menon underlined, making it clear that while there was no proof of India interfering in the internal affairs of Pakistan, the reverse was not true.
At a separate briefing for the media, Pakistan Foreign Secretary Jalil Abbas Jilani termed the talks "positive and constructive, but took the line that a "peaceful sustained and uninterrupted dialogue" was the way to resolve issues between them.
"There is no alternative to a peaceful sustained and uninterrupted dialogue. We need to have an interaction on a regular basis to address all our outstanding issues," he said.
The two prime ministers tasked the Director Generals of Military Operations (DGMOs) of both countries to come up with "effective measures" to restore the 2003 ceasefire on the Jammu and Kashmir border, the Indian national security advisor told media.
"The decision was for DGMOs to come up with real plans to restore the ceasefire."
Menon said Sharif raised issues of concern to Pakistan including the disputed Siachen glacier and Sir Creek.
"Our overall impression was that the meeting was useful, it provided an opportunity to discuss issues that are troubling the relationship," he added.
Sharif invited the Indian prime minister to visit Pakistan, and Manmohan Singh -- who was born in what is now the Pakistani Punjab -- reciprocated. No dates have been set for their visits.
Menon acknowledged that while the two leaders desire a better bilateral relationship, they were "also conscious of the difficulties standing in the way".
On the issue of terrorism, saying that it affected them both Jilani made no promises and instead harped on Kashmir and spoke of "external interference" without naming India.
"Terrorism was discussed. We are aware of your concerns on terrorism, and I think our concerns are also known to the Indian side," he said in response to a question fromn Indian media.
Asked about Manmohan Singh's description of Pakistan as the "epicentre of terrorism" Jilani said: "It was not raised during the meeting. Terrorism was discussed but not in the context that you are talking about."
"Prime Minister Sharif also emphasised on external interference in Balochistan and other parts of Pakistan," Jilani said.
Describing Kashmir as a "very important issue" that needs to be resolved, Jilani said: "We witnessed an equal willingness on the part of the two leaderships to discuss things in an amicable manner."
Responding to questions on Mumbai attack mastermind Hafeez Saeed and his organisation Jamaat-ud-Dawa (JuD), Jilani parried saying there is "willingness and commitment" on the part of both sides to discuss the issue of terrorism.
The schools and other educational institutions being run by JuD have now been taken over by provincial government of Pakistan at the direction of Islamabad in compliance with the UN Security Council resolution in this regard.
Jilani also claimed that the monitoring team of the UN which had recently visited the country in its report had found nothing about Pakistan violating the UN Security Council resolution in this regard.