Gen Sharif, who arrived in Kabul met Afghan President Ashraf Ghani and other civil as well as military leaders during day-long trip.
Pakistan Army spokesman Lt Gen Asim Saleem Bajwa in a series of tweets, said that both sides discussed coordinated counter-terrorism operations on respective sides and way forward for Afghan peace process.
"With shared responsibility, all stakeholder to support and ensure success," he said on the quadrilateral format of meeting between Afghanistan, Pakistan, China and the US.
A quadrilateral meeting of Afghanistan, Pakistan, China and the United States was held in Islamabad on December 9, on the sidelines of the Fifth Heart of Asia Ministerial Conference.
The first round of quadrilateral meeting will be held in 1st week of January to work out comprehensive road map for meaningful peace, Bajwa said without mentioning its venue.
He said the meeting agreed that that would pursue peace and reconciliation with Taliban groups willing to join the process. "Elements who would still continue to pursue violence will be dealt,under a mutually agreed framework," Bajwa tweeted.
Earlier, he said that Gen Sharif had gone to Kabul "with all the sincerity and optimism for better border management and peace process in Afghanistan."
His visit takes place after Ghani visited Islamabad this month for the Heart of Asia conference and met senior Pakistani leaders including Prime Minister Nawaz Sharif, leading to thaw in tense bilateral ties.
Kabul wants Islamabad to exercise its influence on militants to shun violence and join the mainstream political system by accepting the Constitution of the country.
Gen Sharif last time visited Kabul with Prime Minister Sharif in May and that led to first round of talks between Afghan government and Taliban in July.
The next round of peace talks is also expected to be in Murree exurb of Islamabad where first round of talks took place in July.
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