Eduardo Paes said that his city should not pay for high performance athletes.
“That is the role of the federal government,” he said in an interview to be aired on Friday on the television channel ESPN.
Mayor Paes said Rio should be promoting sports for everyone.
However, the mayor said the Olympic Games would be good for the city because of the infrastructure that was being built.
“Rio will have to look after the legacy of infrastructure,” he said, “But it’s unclear who will run the sports centres after the Olympics.”
In the interview with sports journalist Juca Kfouri, Mayor Paes also said it was a “scandal” that top Brazilian sports officials remained in their posts for life.
A year before Brazil hosts the football World Cup, he was also critical of the sport’s world governing body FIFA, complaining “they only care about stadiums”.
In June, he told the BBC that Brazil had “lost a great opportunity” to improve public services when it won the right to host the tournament.
“We should have used the opportunity to deliver good services too,” he said, arguing that Brazil should have seized the occasion to invest in healthcare, education and transport.
Millions of people took to the streets of Brazilian cities in June to protest against corruption and the high cost of preparations for the World Cup.