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.
Zuma said the African Union had asked the court to postpone any action against Bashir due to the chances of his arrest heightening tensions in Sudan, but it had not rejected the warrant.
"The AU has not said we must not arrest Bashir... South Africa respects international law," Zuma said.
Bashir, the only sitting head of state wanted by the ICC, was sworn in on Thursday after his re-election.
His international travel has been reduced since the ICC warrant was issued last year but he has made a point of travelling to friendly nations in the Middle East and Africa, including Saudi Arabia, Libya and Eritrea.
South African officials were not immediately available for comment on whether Bashir had accepted the invitation before the parliament session.
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