Given the growing humanitarian crisis, Sadiq al-Mahdi told journalists on Thursday that Khartoum should be given the chance to show it is serious about addressing the crisis in Darfur.
Head of the opposition Umma Party and one of the leading figures in Sudanese politics since the 1960s, al-Mahdi blamed Darfur's regional government for encouraging extremism.
He proposed they be sacked as a first step to stop fighting which has killed an estimated 30,000 people and displaced over a million others.
"They have been responsible for the current policies that have encouraged this kind of extremism," he said.
However the US Congress says pro-government "Janjawid" militias are committing genocide in a campaign against local rebels opposed to the government.
Sudan denies backing the militia and protests foreign meddling in its internal affairs.
A US-drafted UN resolution, which the Security Council is expected to vote on this week, threatens Khartoum with unspecified sanctions in 30 days if it does not disarm the Janjawid and prosecute their leaders.
"This investigation will answer the question whether this is genocide, whether it is war crimes. It should be national, but with bona fide international standards"
former Sudanese PM
But veto-wielding Security Council members Russia and China have objected to the draft.
Ousted by President Umar Hasan al-Bashir in a 1989 coup, al-Mahdi said Khartoum should also set up a neutral body to investigate the genocide claims.
"This investigation will answer the question whether this is genocide, whether it is war crimes. It should be national, but with bona fide international standards."
Mahdi also called on Khartoum to agree to talks with Darfur rebels and other Sudanese opposition groups to address the issues that have sparked the western uprising at the same time as Khartoum edges towards peace with other rebels in the south.
He said 30 days was enough time for the government to commit to those demands, open up humanitarian access to Darfur and provide security for the displaced.