Hassan al-Turabi had called for President Bashir to surrender to the International Criminal Court on war-crimes charges.
Aid agencies warn of a humanitarian disaster as Omar al-Bashir calls the arrest warrant a "conspiracy."
Uganda, Congo, and south Sudan attacked the Lord's Resistance Army camp in northern Congo on Sunday.
Previous cease-fire attempts have failed to prevent violence. Many say the Sudanese president is trying to prevent a war-crimes indictment.
Several million dollars in ransom is demanded for the release of 11 Europeans seized in Egypt.
Dozens died in the Kalma refugee settlement Monday when government forces attacked, claiming to search for smuggled weapons.
The pending charges by the international court have put the UN on edge, as it fears reprecussions against its peacekeepers in Darfur.