Mario Andrada said the request, which comes in spite of repeated promises the games would not need public money, was necessary because the two governments did not provide the funding they promised to host the Paralympics last September.
"We talked to them and told them the situation and they have said they will help," Andrada told Reuters.
"The deficit in December was 132 million reais and we have reduced it to 117 million so far this year. We negotiated with suppliers and we are talking to the government."
The Rio city government said it was analysing the contracts but the sports ministry strongly denied Andrada's allegations and said it had "complied fully with all its commitments."
"The federal government does not consider that it has anything pending with the Rio 2016 Committee," the ministry said in a statement.
Andrada said the municipal administration promised 150 million reais and paid only 30 million, while the federal government promised 100 million reais and paid less than 60 million.
The Paralympics took place two weeks after the flagship event but lacked sponsors and organisers and struggled to sell the TV rights. That shortfall meant some countries sent reduced teams to Rio de Janeiro.
The Rio Olympics, the first ever held in South America, were considered a sporting success, but like the World Cup held in Brazil two years previously, they have been widely criticised for poor planning and the lack of legacy.
Several of the main venues, including the aquatics centre, are now lying abandoned.
Landmark projects such as a new metro line stopped miles short of the main Olympic Park, and much of the building for the games has come under investigation in a sweeping corruption probe.
Andrada said the Games were an overall success and claimed that every country since Sydney had ended their Olympic year in the red.
"The games cost 2.8 billion dollars," he said. "That deficit of 132 million reais is around 1 percent. As a percentage it is small."
There is no guarantee that either government will be able to pony up the money Andrade claims is owed.
Brazil is currently in a financial bind as it stumbles through its worst recession in almost a century.
(Reporting by Andrew Downie; Editing by Larry Fine)
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