A new elevated bike path that was heralded as a top legacy project of the Rio de Janeiro Olympics has collapsed, killing at least two people.

The accident on the Tim Maia bike path was the latest in a series of problems besetting preparations for the August 5-21 games, which include worries about an outbreak of the Zika virus, political turmoil that threatens to topple President Dilma Rousseff, underwhelming ticket sales and budget cuts amid Brazil’s worst recession in decades.

Municipal secretary Pedro Paulo Carvalho said a third person was thought to be missing after a giant wave apparently swept up a rocky cliff, lifted an approximately 50-metre stretch of the bike path and sent it plunging on to the rocks and sea below.

Rio’s fire department confirmed only the two deaths. Local news media said two other people were rescued alive.

Helicopters fished the two who died out of the water and laid them out on the golden sands of Sao Conrado beach. Initially covered by colourful beach sarongs, they were later shrouded by a sheet of black plastic.

The bodies were left on the sand for hours, and waves periodically washed over them. A crowd of beachgoers gathered around the corpses, while others continued a game of beach soccer nearby.

Joao Ricardo Tinoco identified one of the victims as his brother-in-law, Eduardo Marinho Albuquerque.

He said the 54-year-old father of one was out jogging at the time of the accident. Tinoco’s sister, Eliane, kneeled over the body, kissing his face and begging to be given another moment to “say goodbye” to her husband.

Carvalho said it was too early to tell what caused the accident and said an investigation was under way.

Shoddy construction is a perennial problem in Brazil, where graft is a fixture of many construction projects.

“It’s clear that an accident like this is unpardonable,” Carvalho told the Globo television network.

The entire four-kilometre bike path, which links the tony beachfront neighbourhoods of Sao Conrado and Leblon, is now closed, he said.

Rio Mayor Eduardo Paes, who was in Greece for the lighting of the Olympic torch, was quoted in a statement as also calling the accident “unpardonable”, and saying he was flying back to Rio immediately to follow the investigations into its causes.