The Western region of Darfur is the scene of an almost decade-long insurgency of non-Arab tribes against the government, which they accuse of political and economic marginalization.
The Sudanese Army said last week it had killed Khalil Ibrahim, leader of the Justice and Equality Movement (JEM), as he tried to cross into South Sudan. JEM has confirmed his death.
In a speech marking Sudan's independence day, Bashir called on JEM fighters to lay down their weapons. "If those who break away from what is called the Justice and Equality Movement ... want peace, then our doors and hearts are open," Bashir said. He did not elaborate.
JEM officials could not be reached immediately for comment.
The United Nations has said as many as 300,000 people may have died in Darfur, where Khartoum mobilized troops and mostly militias to crush the uprising. Khartoum puts the death toll at 10,000.
Qatar brokered a peace deal which Sudan signed this year with the Liberation and Justice Movement (LJM), an umbrella association of smaller groups. But JEM and the other major rebel groups have refused to sign the document.
In November, Darfur's main insurgent groups and rebels in two border states said they had formed an alliance to topple Bashir.
