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According to a report by Dawn, there was, however, no immediate breakthrough on the pressing issue of reopening the border crossings that Pakistan shut after last month's spike in terrorist attacks, blamed on terrorists with sanctuaries on Afghan soil.
The two sides, nevertheless, agreed to take "tangible" confidence building measures related to each other's concerns.
Sources in the Pakistani High Commission said the Wednesday's interaction was "positive, productive and held in a cordial atmosphere". They said Pakistan had raised the issue of Afghan-based groups involved in terrorist activities in the country, such as the recent attacks in Lahore and Sehwan.
The meeting between PM's Adviser on Foreign Affairs Sartaj Aziz and Afghan National Security Adviser (NSA) Haneef Atmar was facilitated by British NSA Mark Lyall Grant.
Both sides also met on Thursday night.
In a message posted on his Facebook page after Wednesday's talks, Afghan ambassador to Islamabad Dr Omar Zakhilwal said the London meeting was held "to discuss and agree on a mechanism for genuine bilateral cooperation on fighting terrorism, agree on steps and measures to improve the current tense bilateral relations and mutual trust".
"We are positive that the implementation of the mechanism we agreed upon can inject the needed trust and confidence for constructive forward-looking state-to-state relations and cooperation," he added.
Speaking at the weekly media briefing in Islamabad, Foreign Office spokesperson Nafees Zakaria explained that the border closures were "a temporary measure" and steps were being taken to address the challenge of sanctuaries in Afghanistan "so that sooner than later we are able to open the border, and resume the trading of goods and interaction of the people as usual".
"I can't give you the date, but we are mindful and are taking measures which are essential," he said.
The dialogue in London was focused on mutual concerns about existence of terrorist sanctuaries on each other's soil.
Meanwhile Afghanistan based Khaama News also said that a breakthrough has been reported following the meeting hosted by the United Kingdom to defuse the unprecedented tensions sparked between Kabul and Islamabad.
The Office of the National Security Adviser (ONSC) of Afghanistan said some developments have been made as there have been agreements that the meetings will continue in the future.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)