Bashir is wanted by the ICC, of which South Africa is a signatory, over alleged war crimes and crimes against humanity committed during the Darfur conflict dating back to 2003.
The court's president Sidiki Kaba said in a statement that he "calls on South Africa, which has always contributed to the strengthening of the Court, to spare no effort in ensuring the execution of the arrest warrants."
Officials in Johannesburg declined to confirm Bashir's arrival for the two-day summit, but the South African Broadcasting Corporation (SABC) said in a tweet that Bashir had been "welcomed by South African officials and Sudanese diplomats".
The Sudanese state news agency also confirmed the trip.
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Since his indictment in 2009 Bashir has mostly travelled to countries that have not joined the ICC.
Darfur erupted into conflict in 2003 when insurgents mounted a campaign against Bashir's government, complaining their region was politically and economically marginalised.
Khartoum, however, disputes the figures, estimating the death toll at no more than 10,000.