According to spokesman Fred Eckhard, those identified on Tuesday must appear before the ICC in accordance with the terms of last week's UN Security Council resolution.
The commission established that war crimes and human rights violations had been committed in Darfur, while falling short of the definition of genocide.
The body had already handed the list of suspects to Annan under seal. However, Sudan refused earlier on Monday to surrender suspected Darfur war criminals to the ICC.
Branding Thursday's resolution demanding prosecution in the Hague of 51 named suspects, including senior officials, a violation of its sovereignty, Khartoum insisted its own courts were competent to try them.
President Umar al-Bashir swore "thrice in the name of Almighty Allah that I shall never hand any Sudanese national to a foreign court".
Sizeable demonstrations rejected
the UN resolution on Darfur
Resolution 1593, passed by the UN Security Council by a 11-0 majority, overrode strong opposition from Sudan to impose international trials for the 51 suspects identified by the UN commission.
A scorched earth campaign waged by the government against rebels has left more than 300,000 dead and 2.4 million people displaced, according to a report by a British parliamentary committee.
A ceasefire signed by both sides a year ago has been widely violated despite the deployment of an African Union monitoring force, prompting ever louder demands from the rebels for the intervention of Western armies with more sophisticated logistics capabilities.
In a separate development, Annan has named four high-level political figures to help promote his ideas for reforming the organisation prior to the UN General Assembly summit in September.
Annan on Monday named as envoys Irish Foreign Minister Dermot Ahern, former Indonesian Foreign Minister Ali Alatas, former president of Mozambique Joaquin Chissano and former president of Mexico Ernesto Zedillo, to help advance his reforms, according the UN chief's spokesman Fred Eckhard.