Part of the elevated cycle lane fell on to the rocks below when it was hit by a big wave last Friday.
Two men who were on the 50m (150ft) concrete section that collapsed died.
Several Brazilian engineering experts said the cycleway was unsafe and should be demolished.
Mr Paes says, however, that he will go ahead with the project, he told Globo television.
He said the same companies that built the cycleway, Concremat/Concrejato, would be in charge of the reconstruction.
But Mr Paes vowed to identify and punish the people responsible for the tragedy.
Last week, he said the cycleway should have been closed to the public on the day of the accident because of the rough seas, which coincided with a full moon and high tide.
Video footage showed how the wave lifted the concrete section, which was not bolted to the concrete pillars, local media reported.
An eyewitness, Damiao Pinheiro, told O Globo newspaper the waves were "huge".
He said: "People stopped on the bike lane. They were taking pictures of the waves - they were huge. Then I saw the biggest one ever.
"It lifted the cycleway and a piece came off. I saw the people falling. It is really sad."
Two bodies were recovered from the sea and laid out on the nearby beach of Sao Conrado.
Rescue teams have continued searching for up to three people who were reported missing.
Rio de Janeiro had committed to linking up all the city's coastal cycle lanes ahead of the Olympic Games. Work started in January 2014.
This section of the project was opened in January and cost 45m reais ($13m; Â£8m).
The Rio Olympic Games will be held between 5 and 21 September. The Paralympics will begin on 7 September and finish on 21 September.
The Mayor of Rio de Janeiro, Eduardo Paes, has said that the coastal cycleway that collapsed last week killing at least two people will be rebuilt for the Olympics in August.