"The international community cannot be part of any cover-up of genocide or crimes against humanity."
The ICC, which is based at The Hague, is expected to make a decision on any arrest warrant by early next year.
Moreno-Ocampo also said al-Bashir has been "inciting violence" over the genocide charges by threatening civilians and African Union-UN peacekeepers operating under the council's authority.
The court last year issued arrest warrants for a Sudanese government minister and for a commander in the government-backed Janjawid group, blamed for many of the atrocities in Darfur.
But Khartoum does not recognise the court and has consistently refused to hand over suspects.
Several African and Arab states have criticised Moreno-Ocampo's attempt to bring Bashir before the ICC and suggested the Security Council should delay any proceedings.
There has been some support among China, Russia, African and Arab nations for invoking the council's power to defer Moreno-Ocampo's prosecution for at least a year, out of fear that an attempt to arrest al-Bashir could cause further chaos in the nation.
Al Jazeera's Kristen Saloomey at the UN in New York says there is concern at the organisation that a warrant could make the situation on the ground in Darfur even more difficult for peacekeepers and aid workers.
Bashir announced a unilateral ceasefire by government forces in the country's western Darfur region earlier in November but anti-government groups dismissed the move as "insincere".
UN officials say up to 300,000 people have been killed since the Darfur conflict erupted five years ago and that around 2.7 million have been driven from their homes.
However, Sudan says 10,000 people have died in the conflict.