In a court order seen today, the Hague-based ICC's judges are asking Pretoria to submit "by no later than October 5 their views on the events" of Bashir's attendance at an African Union (AU) summit.
The order referred in particular to Pretoria's "failure to arrest and surrender" Bashir, a three-judge bench said.
Bashir, who is wanted by the ICC for alleged genocide, crimes against humanity and war crimes in Sudan's Darfur region, jetted into South Africa in mid-June to attend the summit.
Pretoria argues that because Bashir was attending an AU summit he had immunity from prosecution.
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The ICC's judges, after hearing South Africa's submission, can decide whether to take the matter to the court's Assembly of State Parties or the UN Security Council.
Failure to arrest Bashir, who continues to travel around Africa, has met with condemnation by rights groups and governments including the United States.
However, many members of the AU have accused the ICC of targeting only African leaders, and point out that the US and other major powers such as Russia and China have refused to place themselves under the ICC's jurisdiction.