The decision against Bashir, the most senior figure pursued by the Hague-based court since it was set up in 2002, could spark more turmoil in Sudan and the surrounding region.
It could also hurt prospects for peace in Sudan and pit Western powers against backers of the Khartoum government.
Bashir has dismissed the allegations made by the ICC, the world’s first permanent court for prosecuting war crimes, as part of a Western conspiracy.
"They can eat it (the warrant)," he told a crowd of cheering supporters in northern Sudan on Tuesday.
China, the African Union and the Arab League suggest an indictment could destabilise the region, worsen the Darfur conflict and threaten a troubled peace deal between north Sudan and the semi-autonomous south — potentially rich in oil.
ICC Chief Prosecutor Luis Moreno-Ocampo accuses Bashir of orchestrating a campaign of genocide in Sudan’s western region of Darfur, starting in 2003.
U.N. officials say as many as 300,000 people have been killed in the Darfur conflict since 2003, while Khartoum says 10,000 have died.
A further 2.7 million people are estimated to have been uprooted by the conflict, which began when mostly non-Arab rebels took up arms against the government.