Mr Lochte had claimed that he and a group of three other US swimmers had been robbed at a petrol station.
But CCTV footage contradicted that story, showing the men had vandalised the petrol station.
Mr Lochte told Globo TV, Brazil’s largest broadcaster, that he had not lied over what happened.
“I wasn’t lying to a certain extent,” he said. “I over-exaggerated what was happening to me.”
He added that he was sorry, saying: “Brazil doesn’t deserve that.”
The International Olympic Committee (IOC) has set up a disciplinary commission to investigate the incident and the four athletes’ behaviour.
News of the alleged robbery emerged through Mr Lochte’s mother last Sunday.
Mr Lochte then gave an account of the events, saying he and the other swimmers 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.
However, police said a day later that there were inconsistencies in the men’s accounts.
On Wednesday, two of the men, Gunnar Bentz and Jack Conger, were taken off a US-bound plane at Rio de Janeiro airport and questioned by police.
Both were eventually allowed to leave the country. Another swimmer, Jimmy Feigen agreed to pay $11,000 to a Brazilian charity after the incident.
On Friday, Mr Conger said in a statement that Mr Lochte had pulled a metal advertisement in a frame to the ground, but Mr Conger said he was “unsure why”.
He also said Mr Lochte began yelling at guards for an unknown reason. The men then agreed to pay the guards for the damage.
Rio de Janeiro’s mayor Eduardo Paes had told media he felt nothing but “shame and contempt” towards the men for their portrayal of what happened.
In a separate interview with the US network NBC, part of which also aired on Saturday night, Mr Lochte said he felt “hurt” watching footage of his team-mates being taken off their plane. Mr Lochte had already returned to the United States from Brazil.
“I mean, I let my team down and you know, I don’t want them to think I left them out to dry,” he said.
However, he maintained the men were threatened and made to pay.
“Whether you call it a robbery or whether you call it extortion or us just paying for the damages, we don’t know. All we know is that there was a gun pointed in our direction and we were demanded to give money.”