The prosecutor "has concluded there are reasonable grounds to believe that [al-Bashir] bears criminal responsibility in relation to 10 counts of genocide, crimes against humanity and war crimes," the statement said.
But Khartoum immediately dismissed the move against al-Bashir, saying the court had no jurisdiction over its citizens.
|ICC prosecutor wants:
Al-Bashir to be charged with crimes against humanity and war crimes including murder, extermination, forcible transfer, torture and rape
Al-Bashir to be charged with genocide against ethnic groups in Darfur using the full apparatus of the state, the armed forces and the janjawid militias
An arrest warrant to be issued for al-Bashir and the president's property seized and assets frozen
"Everybody know that Sudan has not ratified membership of the ICC ... it is not a member of the ICC and [the court] has no jurisdiction over Sudan," Ali Othman Mohamed Taha, Sudan's first vice-president, said on Monday.
The ICC, based in The Hague, is an independent permanent court that tries persons accused of the most serious crimes of international concern.
ICC judges will now examine the prosecutor's request and determine whether there are reasonable grounds to suggest that a crime within the court's jurisdiction had been committed.
The judges will then decide if they should issue an arrest warrant, a process that could take several months.
Al Jazeera's Steven Cole, reporting from The Hague, said Moreno-Ocampo had on 11 previous occasions applied for warrants of arrest and has not been turned down by the court yet.
But the court does not have a police force and relies on the country where the accused is resident to deliver the accused to The Hague.
And Khartoum has already refused to surrender two war crimes suspects.
The ICC has also never had a successful prosecution in the five years that it has been in operation.
An ICC case against Thomas Lubanga, a Congolese militia leader accused of enlisting child soldiers during the Democratic Republic of Congo's 1998-2003 war, embarrassingly collapsed earlier this month because prosecutors were found to be withholding evidence from the defence.
Fears of fallout
Moreno-Ocampo's accusation against al-Bashir comes amid concerns that tensions in Darfur could reach boiling point and lead to the expulsion of aid workers and peacekeepers in Sudan's western region.
The joint UN-African Union peacekeeping mission in Darfur on Monday ordered the evacuation of all non-essential staff amid fears that they may be targeted.
However, troops in the joint force will remain in the region, the UN-AU mission said.
The UN says up to 300,000 people have died since the conflict in Darfur broke out in February 2003. The Sudanese government puts the toll at 10,000.