The United States Olympic Committee has apologised for the behaviour of four US swimmers involved in a bizarre incident at a petrol station in Rio.
Two of the four, Ryan Lochte and Jimmy Feigen, claimed the group was robbed at gunpoint after their taxi was stopped.
But CCTV footage appears to prove the story was false, invented by the swimmers after they vandalised the petrol station and clashed with staff.
Mr Feigen is still in Brazil but the other three have now left.
Mr Lochte returned to the US on Monday. The other two, Gunnar Bentz and Jack Conger, were pulled off a flight in Rio on Thursday night but were later allowed to leave for the US. They deny any involvement in the false robbery claim.
Mr Lochte had initially said the four were robbed at gunpoint by men disguised as police officers, while returning from a club by taxi.
But Rio's civil police head Fernando Veloso said the four Olympic gold medallists had not been robbed.
"No robbery was committed against these athletes. They were not victims of the crimes they claimed,'' he said.
He told reporters that one or more of the athletes had instead vandalised a toilet in a petrol station and then offered to pay for the damage.
The Americans paid and left after armed security guards intervened, he said.
One guard had justifiably drawn his gun after one of the swimmers began behaving erratically, Mr Veloso added.
He warned that the swimmers, who had repeatedly changed their accounts of what happened, could "in theory" face charges of giving false testimony and vandalism.
But later on Thursday, the men's lawyer Sergio Riera said Mr Bentz and Mr Conger had been allowed to leave the country by a special Olympic court.
"They are on their way to the airport," Mr Riera said.
He "provided a revised statement this evening (Thursday) with the hope of securing the release of his passport as soon as possible," said the US Olympic Committee (USOC).
The USOC statement confirmed the version of events given by Mr Veloso, and added that "the behaviour of these athletes is not acceptable, nor does it represent the values of Team USA".
Four views of Ryan Lochte
"Maybe he's just a lunk, or a doofus, or a Faulknerian idiot man-child, or the real-world analogue of Moose from Archie. There are all sorts of unflattering descriptors that might apply to Ryan Lochte."
"There is a special category of obnoxious American 'bro' that Lochte represents, in his T-shirt and jeans and expensive suede footwear, which he showed off on Instagram that night at the party along with the price tag. 'We're 6k deep here,' he captioned it. Is there anything worse, in any country, than a bunch of entitled young drunks who break the furniture and pee on a wall?"
"It doesn't matter what else Lochte has done in his Olympic career. This cemented his legacy: most embarrassing Olympic athlete."
"He cried wolf and was called on it, and that will be his burden to bear for a good long while - but not his alone. The Ugly American is alive and well in 2016 thanks to this dope."
Earlier, a Rio 2016 spokesman had tried to make light of the case.
"These kids tried to have fun, they tried to represent their country to the best of their abilities," Mario Andrada told reporters.
"They competed under gigantic pressure. Let's give these kids a break. Sometime you take actions that you later regret.
"They had fun, they made a mistake, life goes on."
How the story evolved
Sunday 14 August
- Ryan Lochte's mother tells US media her son has been robbed in Rio de Janeiro
- Mr Lochte gives an account of the events, saying he, Gunnar Bentz, Jack Conger and James Feigen were returning by taxi from a club in the early hours of the morning when they were robbed at gunpoint by men who forced the vehicle to pull over
- The swimmers do not report the incident to police or to the US Olympic Committee, and police officers only get involved after seeing TV reports
Monday 15 August
- Police investigating the case say there are inconsistencies in the men's accounts
Tuesday 16 August
- CCTV footage emerges of the men's return to the athletes' village showing them laughing and joking, and handing over wallets and phones as they go through the security screens
Wednesday 17 August
- Ryan Lochte admits there were inaccuracies in his original account of being robbed at gunpoint, but vehemently denies making the story up
- Judge orders that the passports of the four men be seized before it emerges that Mr Lochte has already left for the US
- Gunnar Bentz and Jack Conger taken off a US-bound plane at Rio de Janeiro airport
Thursday 18 August
- Brazilian police sources tell media outlets that the men invented a story about a robbery to disguise a dispute over a damaged bathroom door at a petrol station in Barra da Tijuca, 16km (10 miles) from the Olympic Park
- CCTV video emerges that appears to show the athletes being detained and ordered to sit on the ground
- Gunnar Bentz and Jack Conger enter a Rio police station for questioning
- Head of Rio's civil police emphatically denies a robbery took place, saying the case centred around an incident of vandalism and payment for damage
- Gunnar Bentz and Jack Conger fly out of Rio, with James Feigen unable to travel as his passport is still held by the Brazilian authorities
Who are the swimmers?
Lochte is one of the most successful swimmers in history, with 12 Olympic medals, and he once had his own reality television show in the US. In Rio, he swam in two events, winning gold in the 4x200m freestyle relay along with Conger.
Feigen won gold in the 4x100m freestyle relay.
Bentz competed in the 4x200m preliminaries, but not the final. He still received a gold medal after the US team's win.