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. His attempts to open a dialogue with the Taliban, mainly via overtures to the Pakistan government which is believed to support it, have failed.
It commits the group to ending its war against Kabul, respecting the Afghan constitution, and ceasing all contact with other armed, anti-government groups.
Hezb-i-Islami is led by warlord Gulbuddin Hekmatyar, best known for killing thousands of people in Kabul during the 1992-1996 civil war.
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.
Hezb-i-Islami has only intermittently been active on the battlefield for some time; its last known major attack was in 2013, when at least 15 people, including six American soldiers, were killed in Kabul.
Saleem said Hekmatyar's associates, including his family, all appeared united behind him and "are not dissenting with their leader." He said a few points in the agreement were still to be thrashed out, and added: "It is strongly possible that we get to the final points tomorrow and finalize the peace negotiations."
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.
