The visiting Pakistani delegation was accorded a rare guard of honour at the White House.
While the meeting, the first between the two leaders, was still underway, a presidential spokesperson said that the President would also seek the release of Shakil Afridi, the Pakistani doctor who has been imprisoned on charges of helping the CIA track down al-Qaeda chief Osama bin Laden in 2011.
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Counter-terrorism and violent extremism are also among the top issues being discussed during the meeting, which was slated for 90 minutes.
It is understood that Obama, during the meeting, told Sharif to bring the perpetrators of the 2008 Mumbai terror attacks to justice.
Obama was also expected to strongly raise the issue of terrorism emanating from Pakistani soil and would stress on the need for Islamabad to cooperate fully on the peace and reconciliation efforts in Afghanistan, as the US prepares to draw down its troops from the country by the end of 2014.
Sharif was accompanied by his National Security Adviser Sartaj Aziz, Foreign Secretary Jalil Abbas Jilani, who has been appointed as Pakistan's next ambassador to the US; Syed Tariq Fatemi, Special Assistant to the Prime Minister and Finance Minister Ishaq Dar.