Five South African Football Association (Safa) officials – president Kirsten Nematandani, acting chief executive Dennis Mumble, Ace Kika, Barney Kujane and Adeel Carelse – were reinstated to their posts on Friday.
The federation's national executive committee (NEC), which met with sports minister Fikile Mbalula, reversed the decision to suspend the senior administrators after they were implicated in a Fifa probe into match-fixing.
"We want to allay the fears of the public," Chimhavi said on Saturday.
"We are not sweeping this issue under the carpet. The NEC is not commenting on the merit or demerit of the match-fixing report by Fifa.
"They are merely tending to the fairness and legality of processes which have to be undertaken to ensure fairness."
Chimhavi said the NEC had forwarded the issue to the Safa legal committee.
Commission of enquiry
"In the meantime, everyone mentioned in the report by Fifa should be presumed innocent until proven guilty," he said. "The president has made it very clear that he wants this issue to be resolved as speedily as possible."
"We as Safa do not want this issue to be hanging over our heads for a long time."
The five officials had been placed on special leave in December after Safa received a Fifa report on 2010 World Cup warm-up matches which were allegedly fixed.
Safa said a commission of enquiry, headed by a retired judge, would be set up to investigate the matter.
The Fifa report was completed by the global body's former head of security, Chris Eaton, after a bogus football development company, Football 4U, provided referees for the World Cup warm-up matches.
The company was later discovered to be a front for an Asian-based betting syndicate headed up by Wilson Raj Perumal, who was convicted of match fixing. – Sapa