Brazil withdrew its bid on Monday just three days before FIFA choose the 2006 hosts at a vote in Zurich.
Brazilian Football Confederation president Ricardo Teixeira said his country would support South Africa's bid on the basis that the favour would be reciprocated for the 2010 tournament.
FIFA said in a statement on Tuesday that the announcement from Brazil "was not entirely unexpected in view of reports circulating in recent weeks.
"We have always made it clear that any candidate may revoke its candidature at any time," said FIFA president Sepp Blatter.
"At no time has any pressure been brought to bear on any national association to present or renounce its wish to organise the World Cup and there are no sanctions foreseen (against Brazil) for such a late withdrawal."
In an editorial in the latest edition of FIFA News Blatter wrote of the possible need to revise the bidding procedure for World Cup finals, perhaps having a system of preliminary eliminations of some candidates before the final phase of the campaign.
Egypt, Ghana, Nigeria and Brazil have all pulled out of the 2006 race. The remaining candidates are England, Germany, Morocco and South Africa.
Soccer's world governing body FIFA said "no sanctions were foreseen" against Brazil for pulling out of the race to host the 2006 World Cup at the 11th hour.
