Two US swimmers left Brazil after testifying about the robbery claims made by their team-mate Ryan Lochte that have caused outrage in Rio.

Brazilians chanted "liar" as Gunnar Bentz and Jack Conger left the police building after a judge lifted an order seizing their passports, allowing them to check in at the airport.

"They did not lie in their statements. They never lied to journalists. They only stayed quiet. They did not know what was going on," lawyer Sergio Riera said.

The last swimmer in Rio, Jimmy Feigen, provided an updated statement to police, US Olympic officials said, and hoped to get his passport back shortly to return home.

Brazilian police said Lochte and his three team-mates were not robbed after a night of partying, and the intoxicated athletes instead vandalised a petrol station toilet and were questioned by armed guards before they paid for the damage and left.

The robbery claim has become the biggest spectacle outside of the Olympic venues in Rio, casting a shadow over American athletes amid an otherwise remarkable run at the Summer Games.

It was also a blow to Brazilians, who for months endured scrutiny about whether the city could keep athletes and tourists safe given its long history of violence.

"No robbery was committed against these athletes. They were not victims of the crimes they claimed," Civil Police Chief Fernando Veloso said.

The police account came in direct contrast to claims from Lochte's lawyer Jeff Ostrow earlier in the week.

He had insisted the swimmer had nothing to gain by making the story up.

Though police appear mostly finished with their probe, the case is far from settled.

Police have said they are considering charges of falsely reporting a crime and destruction of property, both of which can carry up to six months in jail or a fine.

Lochte and his team-mates could face sanctions from USA Swimming, including fines or suspension. The group, as well as Olympic officials, publicly expressed disappointment and said they would further examine the matter.

"We apologise to our hosts in Rio and the people of Brazil for this distracting ordeal in the midst of what should rightly be a celebration of excellence," the US Olympic Committee said.

The saga began when Lochte said that he and Conger, Bentz and Feigen were held at gunpoint and robbed several hours after the last Olympic swimming races ended.

That claim began to unravel when police said investigators could not find evidence to substantiate it.

Then, security video reviewed by police confirmed the athletes vandalised parts of the petrol station, leading to an encounter with people working there.

The video shows one of the swimmers pulling a sign from a wall and dropping it on the ground. A petrol station worker arrives, and other employees inspect the damage. Mr Veloso said the swimmers broke a door, a soap dispenser and a mirror.

The swimmers eventually talk with workers and their taxi leaves. In another sequence, the swimmers appear to briefly raise their hands while talking to someone and sit down.

After a few minutes, the swimmers stand up and appear to exchange something - perhaps cash, as police said - with one of the men.

The footage does not show a weapon, but a police official said two guards pointed guns at the swimmers.

Mr Veloso said the guards did not use excessive force and would have been justified in drawing their weapons because the athletes "were conducting themselves in a violent way".

Police said the swimmers had been unable to provide key details in early interviews, saying they had been intoxicated.

Officers grew suspicious when security video showed the swimmers returning to the athletes' village wearing watches, which would have probably been taken in a robbery.

Bentz and Conger told police that they felt Lochte had lied about the situation in media interviews, according to text of the statements released by Rio police.

"We got pulled over, in the taxi, and these guys came out with a badge, a police badge, no lights, no nothing just a police badge and they pulled us over," Lochte told NBC television the morning after the incident.

"They pulled out their guns, they told the other swimmers to get down on the ground - they got down on the ground. I refused, I was like we didn't do anything wrong, so - I'm not getting down on the ground.

"And then the guy pulled out his gun, he cocked it, put it to my forehead and he said 'get down' and I put my hands up, I was like 'whatever'. He took our money, he took my wallet - he left my cellphone, he left my credentials."