During the meeting on the sidelines of UN General Assembly, Singh raised the issue of terrorism emanating from Pakistani soil and asked Islamabad to do more to curb the cross-border terrorism.
External Affairs Minister Salman Khurshid, National Security Advisor Shivshankar Menon and Foreign Secretary Sujatha Singh were also present at the meeting. From Pakistani side, Sharif's Advisor on Foreign Affairs Sartaj Aziz was among those who attended the meeting.
The talks came days after twin terror strikes near Jammu that left 10 people dead, mostly security personnel, virtually threatening the highest-level meeting between the two sides.
Singh, who was under pressure from opposition BJP to call off the meeting in the wake of attacks, went ahead with the talks, saying such strikes cannot derail the dialogue process.
However, in a hard-hitting speech yesterday at the UN General Assembly, Singh asked Pakistan to shut down "terrorist machinery" on its soil while making it clear that there can "never, ever" be a compromise on the territorial integrity of India of which Jammu and Kashmir is an integral part.
Singh went ahead with the talks despite facing a strong opposition back home
He virtually rejected Sharif's demand for resolution of the Kashmir issue on the basis of UN Security Council resolutions, saying India favoured settlement of all issues on the basis of the Simla Agreement.
"India is committed sincerely in resolving all issues with Pakistan, including the issue of Jammu and Kashmir, through bilateral dialogue on the basis of Simla Agreement," he said. India considers the UN resolutions as outdated.
Singh said terrorism remained a grave threat to security and stability everywhere and extracts a heavy toll of innocent lives around the world.
"State-sponsored cross-border terrorism is of particular concern to India, also on account of the fact that the epicentre of terrorism in our region is located in our neighbourhood in Pakistan."
Ahead of the meeting, a controversy erupted today over the purported remarks of Sharif calling Singh a "dehati auraat" (village woman).
The controversy has its roots in a comment by a Pakistani journalist that Sharif had used this description "dehati aurat" during a breakfast meeting with him and an Indian TV journalist while expressing his unhappiness that Singh complained to US President Barack Obama on Pakistan.
Later, the Pakistani journalist as well as diplomats denied that Sharif had never made any such remarks on Singh.