Ataul Rahman Saleem, deputy head of Kabul’s High Peace Council, said the deal with the armed wing of Hezb-i-Islami followed two years of talks.
A senior representative of Hezb-i-Islami, Amin Karim, also said he expected President Ashraf Ghani to approve the final version.
Ghani has been trying to forge peace with groups fighting to overthrow the Kabul administration. His attempts to open a dialogue with the Taleban have failed.
While Hezb-i-Islami has been largely dormant in recent years, the deal could be a template for any future deal with the Taleban. It commits the group to ending its war against Kabul, respecting the constitution and ceasing all contact with other armed groups.
Hezb-i-Islami is led by Gulbuddin Hekmatyar, known for killing thousands of people in Kabul during the 1992-96 civil war.
Under the agreement he could soon return to Kabul to sign a formal peace deal and take up residence.
Hekmatyar is designated a “global terrorist” by the US and blacklisted by the UN along with Osama bin Laden. The agreement obliges the Afghan government to work to have the restrictions lifted.
Hezb-i-Islami has been only intermittently active for some time; its last major attack was in 2013, when at least 15 people, including six US soldiers, were killed in Kabul.
Saleem said a few points were still to be thrashed out.
Negotiations began in July 2014, Karim said, when Hekmatyar received a letter from Ghani, then seeking to be president, noting that one of Hekmatyar’s key conditions for peace – withdrawal of all foreign troops – was about to be met.
“That was the beginning,” Karim said.
Progress stalled after President Barack Obama decided to leave a 10,000-strong force in the country to the end of 2016 until Hekmatyar dropped the condition.
Karim and Afghan officials have said a peace agreement with Hekmatyar’s group could encourage Taleban fighters to end their participation in the war, and lead to full peace.