The six-time gold medallist had claimed that he and three other US swimmers had been robbed at a petrol station, but CCTV footage contradicted that story, showing that the men had vandalised the premises.
When asked by NBC's Matt Lauer why he had "left details out", Lochte replied: "I don't know why. It was still hours after the incident happened. I was still intoxicated.
"I'm not making an excuse, I'm not doing that at all, and I shouldn't have said that. I over-exaggerated that part, and the gun was drawn but not at my forehead. It was towards my general direction as you can see in the surveillance video."
Lochte also gave his "deepest apologies to the people of Brazil".
"They put on a great Games. The people of Rio, the people of Brazil, they put on a great Games, and my immature, intoxicated behavior tarnished that a little. And I don't want that. I hope they can accept my apology," he said.
The International Olympic Committee (IOC) has set up a disciplinary commission to investigate the incident and the four athletes' behaviour.