"I really think that's ridiculous,'' Martin's mother, Sybrina Fulton, said on NBC's "Today" show. "I wish Trayvon was here to tell his side of the story. I don't believe that it's God's plan for [Zimmerman] to kill an innocent teenager.''
In an interview that aired on Fox News Channel Wednesday night, Zimmerman said he was not "a racist" or "a murderer" and asserted his killing of the unarmed black teenager was "God's plan."
"I'm not a racist and I'm not a murderer," Zimmerman, a former crime-watch volunteer charged with second-degree murder in Martin's death, said in the recorded interview.
Martin's father, Tracy Martin, said on the "Today" show Zimmerman "had no regards for Trayvon's life, and he don't regret taking Trayvon's life. Had George Zimmerman stayed in his vehicle, Trayvon would be with us here today.''
Zimmerman said he believed he was owed an apology by the Rev. Al Sharpton, film producer Spike Lee and others who he said rushed to judgment and stirred up public sentiment against him. Sharpton and Lee had no immediate comment.
Zimmerman is a white Latino. Martin was black.
Zimmerman, accompanied by lawyer Mark O'Mara, told Fox News he would tell Martin's parents "I'm sorry" but he also said he regretted nothing related to the Feb. 26 killing.
"Do you regret getting out of the car to follow Trayvon that night?" he was asked.
"No sir," Zimmerman said.
"Do you regret that you had a gun that night?"
"Do you feel you wouldn't be here for this interview if you didn't have that gun?"
"You feel you would not be here?"
"I feel it was all God's plan and for me to second guess it or judge it ..."
"Is there anything you might do differently in retrospect, now that the time has passed a little bit?"
Zimmerman, 28, shot Martin as he was walking to the home of his father's girlfriend from a convenience store in Sanford, just north of Orlando. He later told police he shot Martin in self-defense.
Zimmerman told Fox News he didn't at first feel threatened and he said Martin threw the first punch.
As the two struggled, Martin told him, "You are going to die tonight, [expletive]," Zimmerman said.
He said Martin took one of his hands off Zimmerman's mouth "and I felt it going down my chest toward my belt and my holster, and that's when I -- I didn't have any more time."
"Trayvon is a 17-year-old child, and I can't imagine him saying something like that,'' his mother said. "He was frightened for his life.''
Martin's father disputed Zimmerman's assertion he and Martin were fighting over Martin's gun.
"Those are the words of George Zimmerman," Martin said. "George Zimmerman said they were fighting over the gun. There are no witnesses to say they were fighting over the gun. George Zimmerman is here to tell his story. Trayvon is dead.''
Zimmerman said he did not know of Florida's Stand Your Ground law before the shooting.
The law -- one of 21 such laws around the country -- gives the benefit of the doubt to people who claim self-defense when they have a reasonable belief they are in imminent danger of being killed or badly injured.
Zimmerman said if he could talk with Martin's parents, "I would tell them that, again, I'm sorry.
"I don't have -- my wife and I don't have any children," he said. "I have nephews that I love more than life. I love them more than myself. And I know when they were born, it was a different, unique bond and love that I have with them. And I love my children, even though they aren't born yet.
"And I am sorry that [Martin's parents] buried their child. I can't imagine what it must feel like, and I pray for them daily."
He said he was "open" to talking with them at some point.
On Thursday, Zimmerman called in to the ABC show "The View" but co-host Barbara Walters refused to interview him.
Walters had gone to Florida Wednesday for a possible interview with Zimmerman, the Orlando Sentinel reported.
"Barbara went down there to discuss doing an interview, and was prepared if that worked to do an interview," an ABC News spokesman said Thursday. "Mr. Zimmerman made a request that we could not, and could never, agree to. So Barbara walked away."
The New York Post reported Zimmerman had demanded ABC put him and his wife up in a hotel for a month, the Sentinel said.
When Zimmerman called in to "The View" Thursday, Walters told him: "If you could not do the interview yesterday, I don't think we should do a quick one today. But if in the future, if you feel differently, we will consider it."
If convicted of second-degree murder, Zimmerman could face life in prison.