Mr Bashir is the first sitting president to face an ICC arrest warrant
Sudan's highest religious authority has said President Omar al-Bashir should not go to the annual Arab summit in Qatar later this month.
The fatwa (or ruling) was issued by the Committee of Islamic Scholars, citing threats from Sudan's enemies.
President Bashir risks being detained if he leaves Sudan under the arrest warrant issued by the International Criminal Court earlier this month.
He has, however, travelled to Eritrea which is not a signatory to the ICC.
This is his first foreign trip since the arrest warrant was issued.
"He is meeting with President Isaias [Afewerki], and they are discussing bilateral relations. Why should we worry about the ICC issue?" Eritrean Information Minister Ali Abdu told Reuters news agency.
Mr Bashir is wanted to stand trial for alleged war crimes and crimes against humanity in Darfur.
The Sudanese government said shortly after the ICC decision that he would defy the warrant by travelling to the summit in Qatar which is also not an ICC signatory.
But analysts say more recent statements have raised questions over the wisdom of the trip, prompting speculation that another representative may be sent instead.
At the weekend the United Nations presented the Sudanese government with an assessment of the impact of its expulsion of 13 international aid agencies from Darfur.
Khartoum kicked out the groups in the wake of the war crimes indictment of President Bashir.
After two weeks touring the region with Sudanese officials, the UN found that in some camps two months' worth of food had been distributed, but without the complex monitoring to ensure that it goes to those most in need.
The difficult process of therapeutic feeding for the worst nourished children was also not taking place.
Water pumping was continuing, but UN officials pointed out that without the pumps being serviced, they were likely to break down.
And residents in one camp at Kalma, housing more than 80,000 people, said they would reject all humanitarian assistance until the foreign aid groups were allowed back in.
The conflict in Darfur flared into open violence in 2003 when black African rebel groups took up arms against the government in Khartoum, complaining of discrimination and neglect.
Pro-government Arab militias then started a campaign of violence, targeting the black African population.
The UN says this has led to some 300,000 deaths and forced more than two million people from their homes.
The US has said this amounts to a genocide but the ICC rejected a request to charge Mr Bashir with genocide.
The government has always denied charges that it helped organise the militia attacks.
Mr Bashir has been charged by the ICC with two counts of war crimes: Intentionally directing attacks against civilians and pillaging.
He is also accused of five crimes against humanity counts: Murder; extermination; forcible transfer; torture and rape.