"I'm the guy who pulled the trigger that fired the round that hit Harry," Cheney told Fox News Channel, referring to 78-year-old Harry Whittington, who has been hospitalized since the accident.
It was Cheney's first public comments since the shooting Saturday in south Texas.
Cheney has been roundly criticized for failing to tell the public about the accident until the next day. He said he thought it made sense to let the owner of the ranch where it happened reveal the accident on the local newspaper's Web site Sunday morning.
"I thought that was the right call," Cheney said. "I still do."
Cheney said he agreed that ranch owner Katharine Armstrong should make the story public because she was an eyewitness, because she grew up on the ranch and because she is "an acknowledged expert in all of this" as a past head of the Texas Parks and Wildlife Department. He also agreed with her decision to choose the local newspaper as the way to get the news out.
"I thought that made good sense because you can get as accurate a story as possible from somebody who knew and understood hunting and then it would immediately go up to the wires and be posted on the Web site, which is the way it went out and I thought that was the right call," Cheney said.
"What do you think now?" he was asked.
"I still do," Cheney responded. "The accuracy was enormously important. I had no press person with me."
Check out the Texas Parks and Wildlife Department's report on Cheney shooting Whittington (.pdf).
Read and comment about coverage of this story in Public Eye.
A source close to the administration told CBS News correspondent Gloria Borger that people within the White House are livid and that signals are being sent to the vice president's office that the issue has been handled poorly.
Other Republicans defended the vice president. Appearing on CBS News' The Early Show, GOP strategist Bay Buchanan said Cheney was under no obligation to inform the national press about what happened.
"He did everything correct," Buchanan said. "They feel that they have a right to all information about his life, and they simply do not."
She added, "This was a hunting accident. He reported it to authorities immediately and investigation followed."