The issue was raised before the delegation of the United States officials led by Secretary of Defense James Mattis, who arrived in Pakistan on Monday.
In his discussion with Mattis, Abbasi said the two allies shared objectives.
Mattis, who held talks with the Pakistani civil and military leadership on Monday, said the goal of his visit was to find common grounds in order to create a positive, consistent and long-term relationship with Pakistan.
"We're committed (to) the war against terror", he said.
Both sides, the sources added, agreed to take Afghan President Ashraf Ghani into confidence to establish peace in Afghanistan.
His visit to Pakistan comes days after the 2008 Mumbai attack mastermind Hafiz Saeed was released from house arrest.
A United States defence official, speaking on condition of anonymity, said Mattis's conversations had been "straightforward" and specific.
They chose to continue efforts for Afghan peace.
Last week, the commander of U.S. forces in Afghanistan, General John Nicholson, said Islamabad had not carried out the "clear" demands that had been made by Washington.
The Pakistani officials have offered condition support to help end the cross-border attacks in Afghanistan by the militants using the Pakistani territory. Any foreign action on Pakistani soil is not acceptable, Mattis was told.
Refusing the concerns of neighbouring countries, he said that the China-Pakistan Economic Corridor (CPEC) was a game changer project, which will benefit the entire region. "We have eliminated safe havens from Pakistan's soil but are prepared to look into the possibility of miscreants exploiting Pakistan's hospitality to the Afghan Refugees to the detriment of our Afghan brothers", it said. His fierce criticism sparked anti-US protests in Islamabad.
Mattis' brief visit to Islamabad comes a week after a hardline Pakistani Islamist group called off nationwide protests after the government met its demand that a minister accused of blasphemy resign.