The impasse showed no signs of easing up even after Defence Secretary James Mattis visited Islamabad on Monday.
In his discussion with Mattis, Abbasi said the two allies shared objectives.
He added that in his long association with Pakistan, he was aware of the sacrifices rendered and lives lost in Pakistan's fight against terrorism. We are still suffering very badly from the Afghan war. "Nobody wants peace in Afghanistan more than Pakistan".
His visit to Pakistan comes days after the 2008 Mumbai attack mastermind Hafiz Saeed was released from house arrest.
Chances for resumption of the stalled process went further dim following death of Mullah Omer's successor, Mullah Mansur in a US drone strike a year ago in southwestern Pakistan near the Afghan border.More news: Independents not on board with GOP tax plan
They made a decision to continue efforts for Afghan peace.
The Pakistani officials have offered condition support to help end the cross-border attacks in Afghanistan by the militants using the Pakistani territory. United States officials say they will not be able to assess if Pakistan has made progress and fulfilled its promises to prevent the Haqqanis from crossing into Afghanistan until then.
While there may not be any free lunches in this world, Pakistan continues to nearly rever China - a fact underlined by Foreign Minister Khawaja Asif on Tuesday when he said the focus of Pakistan's foreign policy must shift away from the USA and onto China.
"In the absence of the Pakistanis achieving that, we're going to do everything we can to make sure that safe haven no longer exists", said Pompeo.
"If the U.S. could take these two steps, Pakistan would guarantee that its soil would never be used for any militant activities across the Afghan border", a source privy to the details of the meeting said.
President Donald Trump first signalled that the U.S. was reassessing its fractious relations with Pakistan in August when he accused Islamabad of harbouring "agents of chaos". His fierce criticism sparked anti-US protests in Islamabad.