"My former nephew is welcome at the Goodson Anger Management home anytime," Sheen told ABCNews.com, inviting Jones to appear on his FX series, "Anger Management," in which he plays therapist Charles Goodson.
The former "Two and a Half Men" star also said, "It is radically clear to me that the show is cursed," and called Jones' video testimonial against the show a "Hale-Bopp-like meltdown."
Jones apologized for bashing the show late Tuesday, telling the Hollywood Reporter, "Without qualification, I am grateful to and have the highest regard and respect for all of the wonderful people on 'Two and Half Men' with whom I have worked and over the past 10 years who have become an extension of my family."
He said he regretted any indifference or disrespect that his remarks might have implied, and called his "Two and a Half Men" gig an "extraordinary opportunity of which I have been blessed."
Jones' 15-minute-long sit down with pastor Christopher Hudson, who hosts the online show ForeRunner Chronicles, went viral after Hudson posted it to YouTube Monday. While most of the video is devoted to Jones' testimonial about becoming a Seventh-Day Adventist, he goes on a tirade about "Two and a Half Men," where he's played happy-go-lucky kid Jake Harper since 2003.
"Jake from 'Two and a Half Men' means nothing," he says. "He is a non-existent character. If you watch 'Two and a Half Men,' please stop watching 'Two and a Half Men.' I'm on 'Two and a Half Men' and I don't want to be on it."
He goes on, "Please stop watching. Please stop filling your head with filth, please. People say it's entertainment ... the fact that it's entertainment ... do some research on the effect of television on your brain and you'll have a decision to make."
"It's bad news," he adds, shaking his head. "A lot of people don't like to think about how deceptive the enemy is."
That "enemy" has made him rich. According to the Hollywood Reporter, the 19-year-old actor earns about $350,000 per episode, and received a raise along with co-stars Jon Cryer and Ashton Kutcher when the show was renewed for a tenth season in May. "Two and a Half Men" tapes about 20 episodes per season and has been on for 10 seasons.
Representatives for CBS and Warner Bros., the studio that produces "Two and a Half Men," have yet to comment on the video. Hudson said he spoke with Jones on Monday and the actor is "doing very well."
"He's maintaining very well," Hudson told ABCNews.com. "From speaking to him, he was very cool and calm and he's doing very well."
Angus T. Jones Not Due on 'Two and a Half Men' Set for Weeks
What happens now? "Two and a Half Men" managed to muddle out of an epic drama with Charlie Sheen two years ago when Sheen's erratic behavior led to CBS and Warner Bros. booting their star from what was TV's No. 1 sitcom. Sheen went on a media tour afterwards, slamming the show and its creator Chuck Lorre. By all accounts, it was a PR nightmare.
Matt Belloni, news director of The Hollywood Reporter, doesn't think the same thing will happen with Jones. He noted that no studio would want to fire an actor for expressing his religious beliefs. But, he said it's likely that Lorre and the show's producers will ask Jones if he wants out.
"Nobody wants someone who doesn't want to be there," he said. "He's paid very well, they treat him like a professional, it's not like there's some raging feud happening on the set like there was with Charlie Sheen. I could see them working something out where he leaves gracefully."
Jones has time before he has to show his face on set. A source close to "Two and a Half Men" told ABCNews.com that Jones does not appear in the next two episodes being filmed. His character recently joined the Army and hasn't appeared often this season.