He faced the possibility of arrest because of an International Criminal Court (ICC) warrant on charges of genocide.
A South African court ordered Mr Bashir to stay in the country while it decided if the warrant should be carried out.
But before the court ruled, Mr Bashir flew out of South Africa.
Sudan’s president was in South Africa for an African Union summit and the government was aware that it might have been obliged to arrest him, as it is a member of the ICC.
The government argued that Mr Bashir was covered by diplomatic immunity while he was at the summit.
South Africa’s Sunday Times newspaper quotes a government source as saying that at a meeting of security ministers it was agreed that South Africa would protect Mr Bashir “even if it meant flouting court rulings and undermining the constitution”.
In a statement, the government “categorically denies there was a secret meeting” and ads that it will give the court an explanation of how Mr Bashir came to leave the country.
The High Court has given the government until Thursday to reveal how he was allowed to depart.
South Africa’s main opposition Democratic Alliance has said that it will raise the issue in parliament today, first with the foreign affairs minister and then in a debate.
It alleges that Mr Bashir was given assurances that he would be protected “from the highest level”, DA foreign affairs spokesman Stevens Mokgalapa told the BBC’s Newsday programme.
