The understanding came at a meeting between the two sides at the Foreign Office in Islamabad on Thursday.
Foreign Minister Shah Mahmood Qureshi led the Pakistani delegation while the Afghan side by Mullah Abdul Ghani Baradar.
In his remarks, Shah Mahmood Qureshi emphatically stated that Pakistan will continue to sincerely play the role of facilitator to make the Afghan peace process successful.
The Afghan Taliban delegation hailed Pakistan's facilitator role in the peace process.
Shah Mahmood Qureshi stressed that revival of the peace process is important to pave the way towards durable peace and stability in Afghanistan.
The Foreign Minister said war is no solution to any problem. Dialogue is the only way forward for peace in Afghanistan.
Shah Mahmood Qureshi said Pakistan has sincerely played the role of facilitator in the Afghan peace process. He said a peaceful Afghanistan is imperative for regional peace and stability.
The Foreign Minister said instability in Afghanistan is adversely affecting both Pakistan and Afghanistan. He said the world is now also endorsing Pakistan's stance on Afghanistan.
Shah Mahmood Qureshi pointed out that Pakistan-Afghanistan relations are rooted in common history, faith and culture. He said Pakistan has been hosting the Afghan refugees over the last four decades.
Earlier, Foreign Minister Shah Mahmood Qureshi and senior officials welcomed the twelve member Afghan Taliban delegation as it arrived at the Foreign Office.
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