An official privy to the development has told The Associated Press that the new demands include cancellation of pacts with the United States, a timetable for the withdrawal of foreign troops and that it be signed by a new government.
A member of Hezb-e-Islami negotiating team has said the demands were made in a letter to President Mohammad Ashraf Ghani.
Earlier, Hekmatyar said he has changed his conditions for peace process with the Afghan government by stepping back from his demands for the complete withdrawal of foreign forces.
Hekmatyar was originally demanding the complete withdrawal of the foreign forces from Afghanistan before officials talks begun between his party and the Afghan government.
This comes as the Afghan government has signed the draft peace agreement with Hezb-e-Islami in mid-May amid hopes that the agreement would be signed by Hekmatyar in the near future.
Deputy Chief Executive Mohammad Khan said last month that the party has agreed to have no links with the anti-government armed militant groups, insisting that Hekmatyar’s only demand is to remove his name from the international blacklist.