If the arrest warrant is granted, it would be the first issued by The Hague-based court against a sitting head of state.
However, Khartoum does not recognise the jurisdiction of the ICC and had previously refused to hand over suspects demanded by the court.
"We will not submit our president to any kind of questioning or answering to a body Sudan is not part of," Malual said.
Ban Ki-moon, the UN secretary-general, has urged Sudan to ensure the safety and security of the peacekeepers, some of whom have already been targeted.
Seven UN peacekeepers were killed when they were ambushed in North Darfur on July 8.
Khartoum's warning came as UN officials said that Sudanese aircraft had bombed the Darfur region this week despite al-Bashir making a highly publicised pledge to restore peace during a visit to the region.
The air raids are said to have taken place in the Tawila area, west of the town of El Fasher, where the UN-led peacekeeping mission in Darfur is based, as well as the Jebel Moon and Jebel Marra areas of western Darfur.
The two areas are respectively strongholds of the Sudan Liberation Movement-Unity and the Justice and Equality Movement (Jem), rebel groups fighting government forces.
|Barely a third of the projected peacekeeping force has been deployed [AFP]
Jem claimed responsibility for an attack on the Sudanese capital in May.
There was no immediate information about casualties or damage during the bombings, but the UN mission (Unamid) said it would send a team to investigate.
The conflict began when African ethnic minority rebels took up arms against the Arab-dominated government and state-backed Arab militias, called the Janjawid, fighting for resources and power in the remote region.
According to the UN, at least 300,000 people died and more than 2.2 million have fled their homes since the conflict erupted in February 2003. Sudan says 10,000 have been killed.
The African Union asked the UN Security Council on Monday to delay a decision on whether the ICC should indict Beshir.
The AU handed over its peacekeeping mission in Darfur to the UN on December 31.
So far only 7,600 troops and 1,500 police have been deployed, barely a third of the planned total of 19,500 soldiers and 6,500 police.