Al-Turabi said al-Bashir was "politically culpable" for the conflict there and urged him to hand himself over in order to save Sudan from the sanctions and political turmoil that would follow if he defied the court.
The ICC issued a warrant on Wednesday, charging al-Bashir with seven counts of war crimes and crimes against humanity for his involvement in the Darfur crisis.
Hours after returning home on Monday, al-Turabi expressed his support for the ICC decision.
"I am a man of law, I believe in international justice," he said. "We accept international justice, whether it is for us or against us.
"I read of course the memo of Ocampo [the ICC prosecutor], and I think it was really substantial ... I knew that it would not be rejected completely."
The UN estimates 300,000 people have died since conflict broke out there in 2003, when ethnic minority rebels took up arms against the Arab-dominated government for a greater share of resources and power.
Al-Bashir has rejected the charges and refused to turn himself over to the court, which is not recognised by the Sudanese government.
Al-Turabi was one of al-Bashir's closest advisors when he took power in a bloodless coup in 1989.
But the two split over the introduction of a bill to limit the president's powers in 1999, a move which al-Bashir countered by dissolving parliament and declaring a state of emergency.
Al-Turabi was chairman of al-Bashir's National Congress Party, but was suspended from this post after calling for a boycott of the president's re-election campaign in 2000.
He subsequently formed the Popular National Congress Party, one of Sudan's main opposition parties, which advocates an Islamic state and is critical of Western secularism.
Al-Turabi, a vociferous critic of the government, has been frequently detained, including in 2005 after an alleged coup attempt.