The African Union (AU) has expressed concern over reports that war-crimes charges might be brought against members of the Sudanese government.
The AU said such a move could jeopardise peace efforts in the region.
Thousands of UN and AU peacekeepers are deployed in Darfur and a spokeswoman for the force has said the security alert for its staff has been raised.
Prosecutors at the International Criminal Court are expected to present new evidence on Darfur on Monday.
In a statement issued on Saturday, the African Union "expressed its strong conviction that the search for justice should be pursued in a way that does not impede or jeopardise efforts aimed at promoting lasting peace".
The statement also "reiterated the AU's concern with the misuse of indictments against African leaders".
'Sovereignty violation'
Sudanese officials have reacted angrily to reports that Mr Bashir could face war crimes charges.
They say this would have serious implications on peace and security in Darfur and the rest of the country.
Government spokesman Mahjoub Fadul Badry said an indictment would violate Sudan's sovereignty.
"If an international organisation or the organisations working in the humanitarian field are behind such an indictment of the head of state, our symbol of national sovereignty, then no one should expect us to turn our left cheek," Mr Badry told Al-Arabiya television.
Meanwhile the joint UN-AU force in Darfur has raised the security alert for its staff to "level four", spokeswoman Shereen Zorba was quoted as saying by AFP news agency.
The new security level stops short of evacuating all staff, but foreign workers who are not directly involved in relief or security operations are to be relocated, she added.
She said most Unamid staff are involved in aid or security work so will not be relocated yet.
Under fire
The United Nations-African Union Mission in Darfur (Unamid) has 9,000 troops in Darfur. They have been struggling to contain the violence there.
Seven Unamid troops were killed on Wednesday and 22 injured in an attack on 9 July by suspected members of the pro-government Janjaweed militia.
Over the last five years, more than two million people have fled their villages in Darfur, destroyed by the Janjaweed.
The Arab militia has been accused of ethnic cleansing and genocide against black African civilians, after rebels took up arms in protest at alleged government discrimination in 2003.
The UN estimates that some 300,000 people have died because of the conflict but Sudan's government says the scale of the violence has been exaggerated.
It is estimated that two-thirds of Darfur's surviving population rely on humanitarian assistance.
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