Al-Bashir was indicted on Wednesday by the ICC at The Hague in the Netherlands for war crimes and crimes against humanity committed in Darfur.
Al Jazeera's Yvonne Ndege, reporting from Nairobi, Kenya - Sudan's neighbour and a signatory to the ICC - said the AU's appeals to halt Bashir's indictment have so far been ignored by the international community.
Majok Guandong, Sudan's ambassador to Kenya, said he was confident African nations will not implement the decision by the ICC.
"It will be a contradiction. How can you implement a decision of an organisation that ignores your own opinion," he told Al Jazeera on Friday.
Hours after al-Bashir was indicted he began expelling foreign aid agencies from Sudan, raising fears of a further humanitarian disaster.
Rupert Colville, a UNHCR spokesman, told Al Jazeera that the decision to expel 13 aid agencies from Darfur "could be absolutely disastrous".
"These are the biggest agencies there are in humanitarian work and they're absolutely crucial. They do life-saving work in terms of providing food, clean water, healthcare. Thousands of people could die as a result of the decision [to expel the aid agencies]," he said.
"To punish civilians is a grievous dereliction of the duty of the government to care for its own people, so we absolutely appeal to the government to not link these two events together and let humanitarian work go on."
The ICC is now considering whether to add the expulsion of the agencies as another war crime charge.
The Rome statute that set up the ICC allows the UN Security Council to pass a resolution to defer or suspend for a year the investigation or prosecution of a case.
Moses Wetangula, the Kenyan foreign minister, said the operations of the ICC have been "very suspect".
"Look at the manner in which they have handled African issues. It's not just the ICC in The Hague, the application of so called universal jurisdiction in criminal matters has been laced with some racial undertones," he said.
|There are fears that civilians will suffer as a result of aid agencies' expulsion [AFP]
The Justice and Equality Movement (Jem), the most powerful rebel group in the Darfur region, said it would act on the warrant for al-Bashir.
Ibrahim Khalil, the Jem leader, told Al Jazeera: "They say the ICC does not have a mechanism to arrest him [Al-Bashir]. But we say that Jem has its own great and powerful mechanism..."
"[There is] a mechanism by the Sudanese people, a mechanism of Justice and Equality, a mechanism of co-operation with the international community. We shall fully collaborate with the Security Council and the ICC."
Abdul Wahed al-Nour, the leader the Sudan Liberation Movement/Army (SLM/A) opposition party, told Al Jazeera that his group supported the ICC's move to arrest Bashir.
"We fully support, recognise and will co-operate with the ICC decision and we ask for the international community to co-operate with us in handing over Bashir to the court and help the Sudanese people in avoiding more violence in the country," he said.
"Law and justice must be implemented by the ICC, which can only happen with a strong international wheel behind us."
Al-Bashir has rejected the warrant, telling thousands of his supporters in Khartoum, the capital, on Thursday that Sudan was being targeted by Western powers and that the ICC was a tool of colonialists after Sudan's oil.
The ICC indicted al-Bashir on seven counts of war crimes and crimes against humanity, which include murder, rape and torture.
The three-judge panel said it had insufficient grounds to consider charges of genocide, though the ICC said the non-inclusion of a genocide charge could change "if additional evidence is gathered by the prosecution".
Ban Ki-moon, the UN secretary-general, has urged Sudan to co-operate with the court.
The UN says that up to 300,000 people have been killed in Darfur, where the world body is running one of the world's largest humanitarian missions.
Sudan maintains that only 10,000 people have died.
A further 2.7 million people are estimated to have been uprooted by the conflict, which began when mostly non-Arab rebels took up arms against the government in 2003, saying they were being marginalised.