Bashir is wanted by the International Criminal Court (ICC) on charges of war crimes. He rejects the charges of ordering mass murder, rape and torture in the western Darfur region.
Zuma said in response to a question in parliament that South Africa had a responsibility to arrest him should he act on the invitation, sent to all African leaders, and attend the June 11 opening ceremony.
"South Africa respects the international law and certainly we are signatories (of the ICC statute), we abide by the law," he said in a parliamentary session on Thursday.
"The AU has not said we must not arrest Bashir... South Africa respects international law," Zuma said.
South African officials were not immediately available for comment on whether Bashir had accepted the invitation before the parliament session.
