It added that Sharif told Karzai he agreed on "facilitating the meeting of Mullah Baradar with his family, agreed on his full release, but mentioned that this issue should also be discussed with the Americans."
Pakistan has released around four dozen Taliban prisoners over the last year. It has never said how many it is detaining. The U.S. has in the past expressed concern about the release of Taliban without some way of monitoring their whereabouts.
Sharif said 2014 was a "milestone" as foreign forces depart and Afghanistan takes responsibility for its future and sovereignty. NATO and United Nations mandates that have kept tens of thousands of international forces in Afghanistan since the American invasion in late 2001 expire next year.
"In our view, the key to sustainable peace in Afghanistan in 2014 and beyond is an inclusive political settlement. That is why Pakistan has steadfastly supported an Afghan-led and Afghan-owned peace and reconciliation process," Sharif said. "I take this opportunity to once again urge all the stakeholders to seize this moment and join hands to support the peace efforts. It is imperative to reverse the destructive cycle of conflict."
He assured Karzai "that Pakistan would continue to extend all possible facilitation for the Afghan peace process."
Both men made very short remarks after their meeting and took no questions. Both expressed their general desire for closer ties, trade and regional peace.
Karzai said that working together "Afghanistan and Pakistan will be rescued from terrorism and extremism."
Pakistan is beset by its own Taliban insurgency that has claimed the lives of thousands of soldiers and civilians in recent years.
Sharif's one-day visit was his first to Afghanistan since being elected. Karzai has been pushing Pakistan for help in talking to the Taliban, where many of its leaders are thought to be based. Kabul has sought Islamabad's help to bring the militant group to the table.
Sharif also said they discussed trade and energy issues.
Relations between the two countries have been testy and Afghanistan has often accused Pakistan of aiding Taliban leaders sheltering across the border. Sharif has nonetheless made improving ties with Afghanistan a priority.
The Taliban have refused to talk directly with Karzai, his government or its representatives. U.S.-backed talks between Afghanistan and the Taliban failed in June.
Pakistan has a complicated relationship with the Taliban. It helped the group seize control of Afghanistan in 1996, and Kabul has repeatedly accused Islamabad of providing the insurgents sanctuary on its territory following the U.S.-led invasion of Afghanistan in 2001.
The peace talks have also been the focus of recent tensions with the United States.
Karzai has demanded that America do more to get them started, and said he will not sign a security agreement allowing thousands of American troops to remain in Afghanistan past 2014 if they do not.
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Associated Press writer Rahim Faiez contributed to this report.
