The impasse showed no signs of easing up even after Defence Secretary James Mattis visited Islamabad on Monday.
"We're committed (to) the war against terror", he said.
However, Mattis was told that Pakistan would be ready to take action against any group of militants on the receipt of actionable intelligence from the USA side.
A Pakistani official privy of the development has told the local newspaper, Pakistan Today, that Islamabad would only guarantee no attacks from its soil if the USA special forces erect a fence along Pakistan-Afghan borders and also repatriates all the Afghan migrants. "Nobody wants peace in Afghanistan more than Pakistan".
Pakistan denies the charge and accuses Kabul of allowing militants to use its soil for attacking Pakistani security forces and civilians. USA 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.
A statement released later on Monday from Abbasi's office echoed the term "common ground", and said Mattis had emphasised he was "keenly aware" of the thousands of lives Pakistan has lost in its long battle with militancy.
Pakistan had brokered a landmark round of direct talks between the fragile Afghan government, and the Taliban in Islamabad in July 2015, but the process broke down after the Taliban announced the death of their long-term leader, Mullah Omer, triggering a bitter power struggle within the militant group. "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.
Pakistan is confident that the United States will amend its South Asia strategy announced by President Trump in August this year. His fierce criticism sparked anti-US protests in Islamabad.