Baldwin said, "calling your child a pig, or anything else, is improper and inappropriate, and I apologize to my daughter for that."
He said everyone who knows him knows he has "a great relationship" with his daughter, Ireland.
Baldwin knows "the guy that's responsible" for leaking the tape, but he didn't disclose a name.
The actor previously blamed his former wife, actress Kim Basinger, for the leak, which she denied.
Meanwhile, Baldwin went to TV psychologist Dr. Phil McGraw for family advice after his comments were made public last week, the therapist revealed Thursday.
McGraw said Baldwin gave him permission to disclose that they had a “far-reaching, intense conversation” and that he had also “reached out privately to Basinger.”
On the voicemail tape, which was posted on TMZ.com, Baldwin calls Ireland a “rude, thoughtless little pig” for allegedly ignoring his phone calls and not making enough time for her dad.
“I’ve made an a-- of myself, trying to get to a phone to call you at a specific time,” he said in the message.
"I’m tired of playing this game with you ... You have insulted me for the last time.”
In the two-minute rant, the 49-year-old actor screamed at his daughter, “I’m going to come out there for the day, and I’m going to straighten your a-- out when I see you!”
Baldwin has been in a bitter custody dispute with his Oscar-winning ex since their 2002 divorce.
Also on "The View," Baldwin said there is “nothing wrong with being frustrated or angry about something. It’s the way you do it, and as people often do in this world, I took it out on the wrong person because I’m unable, under the current dynamic, to address the other person.
“I realize that was wrong,” he said.
Baldwin also said he would like to get out of his contract with the NBC sitcom “30 Rock.”
“I hope they will [let me out] go do something else,” he said, explaining that he wanted to focus more on his family, including Ireland and his ailing 78-year-old mother.
“It’s not like my career is something that we’re nipping in the bud; I’ve been doing this for 27 years. I mean, I’ve had enough of this, quite frankly, to last me a lifetime.”
NBC, which has had critical success with the sitcom, in which Baldwin plays a charismatic network executive in charge of a “Saturday Night Live”-type show, shot down his idea.
“Alec Baldwin remains an important part of ‘30 Rock.’ We look forward to having him continue his role in the show,” the network said Thursday.
The New York Post and the Associated Press contributed to this report.