Mr Cheney said he is taking full responsibility for shooting his friend Harry Whittington, but defended his failure to disclose the incident immediately.
"Ultimately, I'm the guy who pulled the trigger that fired the round," he told Fox News Channel.
Mr Cheney had faced mounting pressure from politicians and the media to explain what happened when the group was hunting quail at a Texas ranch over the weekend.
Mr Whittington required immediate medical help before being transferred to intensive care, and later suffered a mild heart attack related to the shooting.
"The image of him falling is something I'll never be able to get out of my mind. I fired, and there's Harry falling and it was, I have to say, one of the worst days of my life," said the vice president.
Mr Cheney defended his decision not to report the matter to the public immediately, the time it took for the incident to be brought to light and his failure to offer an official account until now.
It was not until 21 hours after the shooting that the shooting was made public by ranch owner Katharine Armstrong, who gave details to a local newspaper.
"I thought that was the right call. I still do," said Mr Cheney.
"I had no press people with me, I was there on a private weekend with friends on a private ranch."
It was unclear why the vice president, who never travels without an entourage of security and communications, could not have reached out to staff in Washington or elsewhere.
When reporters contacted his office on Sunday afternoon seeking comment on the local Texas newspaper story, his spokeswoman was able to confirm all of the details but declined to provide an official account.