Pakistan is known for supporting the Taliban and various other terror groups in Afghanistan.
It was unclear if any progress was made in the unofficial meetings with a representative of a prominent Afghan politician. But both the government and the Taliban have tried to distance themselves from the Turkey meeting.
A spokesman for Afghan President Ashraf Ghani said on January 17 he was not aware of the Islamabad talks, while the Taliban did not respond to queries.
However, two senior Taliban officials said on condition of anonymity that supreme leader Haibatullah Akhundzada had approved Monday's exploratory meeting in Islamabad on restarting talks to end the war that kills thousands of Afghans each year. Pakistan believes that the economic and security assistance figures quoted by the president were off the mark.
Ms Wells had suggested to Pakistani leaders that enhanced intelligence cooperation could provide the basis for improvement in ties, especially in counterterrorism cooperation, which is at the heart of the problems in their relations.
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They met representatives of Afghan politician Pir Syed Hamid Gilani, head of the National Islamic Front of Afghanistan and the son former High Peace Council chief who died last July, a senior aide to Gilani confirmed on condition of anonymity.
A media report hints at the two sides agreeing on the so called "carrot and stick' policy vis-a-vis the Afghan Taliban i.e. kudos for those who agree to talks and punishment for those who refuse to come to the negotiating table".
Returning from a UN Security Council visit to Afghanistan, US Ambassador Nikki Haley on Wednesday stressed the Kabul government wants world powers to step up pressure on Pakistan.
Haley said a weekend trip by the Security Council to Afghanistan was "great" because "we could see dramatic changes in terms of what the United States policy has been doing", AP reported.
"Yet, some interlocutress were not too optimistic, claiming that there was no significant steps towards establishing a peace process by the Taliban despite overtures by the government". He will take part in the UN Security Council meetings on non-proliferation of mass destruction weapons and the situation in Afghanistan, TASS reported. "We think the Taliban coming to the table is very important and we think that the entire global community needs to support this process so that we can have peace". "They did ask us for consensus to put further pressure on Pakistan to come to the table and change their behavior", the US Ambassador said.