The call from Islamist leader Hassan al-Turabi was the first significant show of dissent from within Sudan's political system over possible war crimes charges against President Omar Hassan al-Bashir. Most politicians have previously been united in opposing them.
The global court's chief prosecutor asked judges in July to issue an arrest warrant against Bashir, accusing him of genocide and other war crimes. The judges are expected to decide within weeks whether Bashir has a case to answer.
Turabi told reporters Bashir should surrender himself to save Sudan from sanctions and political turmoil that would follow if the president defied the court and carried on ruling as a wanted man.
"There is no judicial justice in this country ... As far as we are concerned there is no access to justice except through the international court," Turabi said in the Khartoum headquarters of his opposition Popular Congress Party.
"It is up to the government to hand him over or for him personally to go for the sake of his country, to protect his country against any further sanctions against the government."
Turabi said he was not saying Bashir had personally orchestrated war crimes in Darfur—just that the president should take political responsibility for atrocities carried out under his leadership.
Turabi, once close to Osama bin Laden, has been a central figure for decades and repeatedly detained and imprisoned. He was the spiritual mentor behind Bashir's government when it took power in a 1989 coup, but the men later fell out.
Turabi said Sudan's many insurgent groups would step up attacks and destabilise the country if Bashir stayed in power without clearing his name.
Conspiracy
Bashir and leading members of his dominant National Congress Party have repeatedly said they will not deal with the global court, dismissing it part of a Western conspiracy.
Most Sudanese opposition parties publicly rallied round Bashir after the ICC's chief prosecutor, Luis Moreno-Ocampo, accused the president of orchestrating genocide and other war crimes in Darfur.
Turabi said on Monday that Bashir should take personal responsibility for atrocities since 2003 in Sudan's west.
"In politics, whatever happens below a minister, for example, he will have to resign for it and assume responsibility," Turabi said. "He should assume responsibility for whatever is happening in Darfur—displacement, the burning of all the villages, systematic rapes."
Turabi said he did not think Khartoum deliberately set out to launch genocide—as Washington and some activists say.
"But they recruited nomadic Arabs—the Janjaweed ... and these people behaved in that manner. When they burned a village they just burned all the boys, killed all the males ... That was systematic. It was not just one case or two."
The influential opposition leader added he did not expect Bashir to take his advice.
International experts say 200,000 people have died and 2.5 million have been forced from their homes since mostly non-Arab rebels took up arms against Sudan's government in 2003, accusing Khartoum of neglect.