In a statement issued on the athlete's Twitter account, Lochte said: "It's traumatic to be out late with your friends in a foreign country...and have a stranger point a gun at you and demand money to let you leave," but admitted he "should have been more responsible."
The 32-year-old said he apologised for "not being more careful and candid" in his description of the events.
He added he was sorry for "taking focus away from the many athletes fulfilling their dreams of participating in the Olympics."
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The US Olympic Committee also issued an apology in a statement on Thursday, saying: “The behaviour of these athletes is not acceptable, nor does it represent the values of Team USA or the conduct of the vast majority of its members. We will further review the matter, and any potential consequences for the athletes, when we return to the United States.
“On behalf of the United States Olympic Committee, we apologize 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.”
Lochte's apology comes as Brazil police announced that Jimmy Feigen, one of the four swimmers involved, had agreed to pay 35,000 Reais to a charity.
Meanwhile the Mayor of Rio de Janeiro said he accepted an apology issued by the US Olympic Committee regarding the incident, but said he had only “pity and contempt” for those involved. He added that their behaviour had damaged Rio’s reputation, but that they did not represent the spirit of other US athletes present at the games.
The four swimmers - Lochte, Feigen, Jack Conger and Gunnar Bentz - said they were travelling home from a night out in Rio when their taxi was pulled over by people posing as armed police. Lochte told NBC: “the guy pulled out his gun, he cocked it, put it to me forehead and he said, ‘Get down,’ and I put my hands up, I was like ‘whatever’.”
He said the assailant took his money and his wallet, leaving his credentials and mobile phone.
Suspicion about their story was aroused after the four men apparently gave conflicting evidence to police, who later sought to stop them leaving the country, pending further investigation. Lochte had already left for the US, though Conger and Bentz were apprehended as they were due to fly out of Rio, while Feigen had remained in the city.

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CCTV footage shown on Brazilian television on Thursday appeared to confirm the four swimmers had not told the whole truth when they said they were robbed at gunpoint.
"The athletes lied to us about their story," a top Rio police official told Reuters on Thursday, declining to be identified because the matter was still under investigation.
A police source and staff at the station have said that the swimmers caused minor damage there. The source said they damaged a bathroom door and staff said they tore down a poster and also urinated on the wall of the station's convenience store.

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The video does not show them causing any breakages, but only being hustled out of the bathroom by uniformed employees. Security guards then prevent the swimmers from leaving in a taxi and the Americans appear to offer them money from their wallets.
Three of the swimmers are made to sit on the ground with their hands in the air. At one point, Lochte stands and appears to argue with the guards but is made to sit down again.
Additional reporting by Reuters.
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