India's new PM meets Pakistan chief
But all eyes were watching the meeting between Mr Modi and Mr Sharif for signs of a thaw in the relations between the nuclear-armed neighbours.
India's foreign secretary Sujatha Singh told reporters: "The prime minister underlined our concerns related to terror. It was conveyed that Pakistan must abide by its commitment to prevent its territory and territory under its control from being used in terrorism against India."
Mr Sharif also addressed reporters, saying that the meeting between the two prime ministers should be "a historic opportunity for both our countries".
Mr Sharif said as leaders with a popular mandate the two men could succeed in "turning a new page" in the often-hostile relations between their countries. He said that both men shared a common goal of economic development which could not be achieved without "peace and stability in the region".
"I urged that we had to strive to change confrontation into co-operation. Engaging in accusations and counter-accusations would be counter-productive, I emphasised," Mr Sharif said, adding that "my government, therefore, stands ready to discuss all issues between our two countries, in a spirit of co-operation and sincerity".
Mr Modi also asked that Pakistan hasten its investigation into the 2008 terror attack on Mumbai, India's financial hub, in which Pakistani militants killed 166 people, and put its perpetrators on trial, Mr Singh said.
Foreign secretaries of both nations will stay in touch and "explore how to move the relationship forward", he added.
The two leaders discussed increasing trade between the nations. The countries have pushed bilateral trade and increased people-to-people contacts even as the thorny issues of terrorism and the status of the disputed Kashmir region remain unresolved.