Ataul Rahman Saleem, deputy head of Kabul's High Peace Council, told The Associated Press that the deal with the armed wing of Hezb-i-Islami could be completed tomorrow, after two years of negotiations.
A senior representative of Hezb-i-Islami, Amin Karim, also said he expected President Ashraf Ghani to approve the final version of the agreement tomorrow.
Such a deal would mark a much-needed success for Ghani in forging peace with insurgent groups fighting to overthrow the Kabul administration.
Hezb-i-Islami is led by warlord Gulbuddin Hekmatyar, best known for killing thousands of people in Kabul during the 1992-1996 civil war.
Also Read
He is believed to be in Pakistan, though Karim has said he is in an unspecified location in Afghanistan. Under the terms of the 25-point agreement, a draft of which has been seen by AP, he could soon return to Kabul to sign a formal peace deal and take up residence.
Hekmatyar, in his late 60s, is designated a "global terrorist" by the United States and blacklisted by the United Nations along with Osama bin Laden. The agreement obliges the Afghan government to do what it can to have the restrictions lifted.
Saleem said Hekmatyar's associates, including his family, all appeared united behind him and "are not dissenting with their leader."
Negotiations began in July 2014, Karim said, when Hekmatyar received a letter from Ghani, then campaigning to become president, noting that one of Hekmatyar's key conditions for peace the withdrawal of all foreign troops from Afghanistan was about to be met.