Abd al-Wahid al-Nur, leader of one faction of the Sudan Liberation Army, rejected the peace agreement signed on May 5 between the government and Minnin Arcua Minnawi, the rival SLA leader.
However on Thursday, Nur said he had written to Salim Ahmed Salim, the African Union negotiator, asking to reopen discussions with the government.
He also said he would sign the agreement if a list of demands were addressed in another document.
"We are ready to sign if there's a supplementary document ... we did this because we want to avoid chaos in Darfur," he said.
He said his demands were more compensation from the Sudanese government for Darfur, greater political representation for his group and more involvement in implementing a ceasefire and disarmament programme.
Alpha Oumar Konare, the African Union Commission chairman, confirmed that an approach had been made by Nur's faction.
"There are no perfect solutions. [We must have] a compromise with guarantees that can improve the solution and that is the only way we can move forward," he said.
The deal was signed in Abuja, Nigeria after weeks of talks and international pressure.
However, Nur's faction and a smaller rebel group, the Justice and Equality Movement (JEM), refused to sign the agreement.
The conflict in Darfur began in 2003 when rebel groups including the SLA and JEM, representing mostly non-Arab tribes, took up arms, accusing the Arab-dominated government of neglect.
Khartoum responded by providing arms to the predominantly Arab militia, known as Janjawid.
Their campaign of murder, arson, rape and looting has left tens of thousands of people dead and more than two million displaced. Khartoum denies responsibility.