According to Amin Karim, an official of the Hezb-i-Islami Party, the party's leader, Gulbuddin Hekmatyar, is no longer demanding that all foreign troops leave Afghanistan.
Hekmatyar is designated a "global terrorist" by the United States and blacklisted by the United Nations. He is widely believed to live in Pakistan, though his supporters say he is in Afghanistan.
Last year, he briefly came out of the shadows to set his conditions for peace that included the withdrawal of foreign forces.
The move by Hekmatyar, whose current following is hard to gauge, is likely as much an overture to the government of President Ashraf Ghani as it is an attempt to stay relevant on the Afghan political scene.
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Hekmatyar has led an extreme life; his mujahedeen followers were responsible for the deaths of thousands during the devastating Afghan civil war. He is said to have offered himself as interlocutor to former President Hamid Karzai in 2008, but was deflected amid concerns over his extremist reputation and human rights abuses.
Ghani came to power in 2014 promising to end the 15-year war with the Taliban. A diplomatic offensive aimed at getting Pakistan to bring the Taliban into peace talks has so far failed, and this year is expected to be as brutal on the battlefield as 2015, when 11,000 civilians were killed or wounded, according to UN figures.
Afghan officials have said that a peace deal with Hekmatyar, a former prime minister of Afghanistan, could be useful in potentially convincing Taliban commanders on the battlefield to join the peace process.