The South African Football Association (SAFA) said it was aware of widespread feeling that a local trainer should have been given the job of leading the side to the 2010 World Cup finals on home soil.
"We are pleading with the public to accept Parreira and let him prepare our team for the World Cup," SAFA vice president Mwelo Nonkonyana said in a radio interview on Monday.
"We are aware of what some leading football personalities and what the public are saying but we believe Parreira is the best choice to lead the team."
The 66-year-old Brazilian, who took his own country to the World Cup in 1994, was South Africa's coach from 2007 to April 2008 but quit when his wife became ill.
He recommended Joel Santana as his successor but after 18 months and growing concern over the form of the South African side, he was fired last week.
Parreira agreed on Friday to return as coach but several former South African national team coaches and weekend columnists hit out at the choice.
The appointment also met with a barrage of abuse from radio callers who said the experiment with Brazilian coaches had failed and that the team's fortunes would be better served with a South African at the helm.
