He also said noted he was extremely embarrassed by the video.
The NFL made multiple attempts to obtain the video of Hunt, but the hotel said corporate policy only allowed footage to be given to law enforcement.
"I just want to let the world know how sorry I am for my actions", Hunt said.
Hunt alluded to someone saying something that upset him, but did not give specifics. The person spoke on condition of anonymity pending a formal statement from the team.
It's unsettling the National Football League has once again decided not to handle the issue of domestic violence in the proper way and that it took a video coming out for the Chiefs to cut Hunt. Belcher was later found to have suffered from CTE.
The video brought immediate comparisons to the footage of former Ravens running back Ray Rice, who was seen punching out his then-fiancée in an elevator. The NFL placed him on the Reserve/Commissioner Exempt List, which would prevent him from playing. The three-time Pro Bowl running back never returned to the NFL. The Redskins made a similar move - and accepted the public backlash - when they signed linebacker Reuben Foster, who had been cut by the 49ers after he was arrested on suspicion of domestic violence.More news: Lion Air crash: Investigators say plane was 'not airworthy'
Salters: When I watch the videos, the lasting impression for me was the kick - you kicking a woman while she was on the ground.
However, a 19-year-old woman named Abigail Ottinger has alleged that Hunt has assaulted her around 3:45 a.m. on Saturday, Feb. 10, at the Metropolitan Hotel. Again, no official charges were filed and Hunt seemed to skate through the offseason.
It's unclear if Ottinger was the woman in the video.
"I regret not getting it all out there", Hunt said, asked what he regretted about the situation. Just, we've got to let you go.
Hunt confirmed that in his interview with ESPN, which aired Sunday, and extended an apology to the team. He ranks fifth so far this year with 824 yards and seven touchdowns in 11 games this season.
When asked during camp about Hunt's off-season incidents, Chiefs chairman Clark Hunt acknowledged that "young men are not always going to make the best decisions".
Hunt said if he could speak with the woman, "I'd want to tell her right now that I am sorry for my actions that night".