Bashir flew out of Pretoria last week after attending a meeting of the African Union despite a court order that barred his departure, sparking international criticism of President Jacob Zuma's government.
Because of what it considers as bias against Africa, the AU has previously urged member states not to cooperate with the ICC.
In parliament, the ANC made its case clear, claiming that because Bashir was attending a meeting of the AU he was entitled to immunity, in the same way heads of state received immunity from arrest in the United States when they attended the United Nations general assembly.
Rather former US president George Bush and former British prime minister Tony Blair should be arrested for war crimes over Iraq, and that leaders of Israel -- which has also not joined the ICC -- should be prosecuted for offences against the Palestinians.
The Sudanese leader has continually denied the ICC charges he committed atrocities in Sudan's troubled western Darfur region.