At least 300,000 people have been killed in the conflict between rebels and government forces that began in 2003. Millions of others were forced from their homes and into displacement camps.
Sudan's decision comes weeks after the ICC's outgoing chief prosecutor, Fatou Bensouda, visited the country and urged its leaders to surrender all those wanted including Mr Bashir, 77.
He was the first person to be charged by the international court for the crime of genocide.
Other ex-officials wanted by the ICC are Former Defence Minister Abdelraheem Muhammad Hussein and former Minister of the Interior Ahmad Harun.
Federal government minister Bothaina Dinar said on Saturday the cabinet's decision was unanimous and aimed at establishing peace and stability in the country.
The government also urged rebel groups to join the peace process.
Source: BBC NEWS
