The 50-year-old actor denied the allegation on Wednesday's episode of The Dr. Oz Show. Richards claims she overheard Sheen telling their daughter Lola, "I'm going to kill you and I'm going to kill your mom," in the $1.2 million lawsuit she filed in January.
"I'm basically being punished for giving her a house," Sheen told host Mehmet Oz. "I would never speak about any of my children like that, ever. And I would never threaten their mom. That's not who I am. I wouldn't do that."
Richards, who shares 10-year-old Lola and 11-year-old daughter Sam with Sheen, is suing the actor for allegedly evicting her from her Beverly Hills home. She claims Sheen threatened her life and sent aggressive text messages to Lola in court documents.
"I don't know. Sure. I probably did. Yeah. And it's regrettable," Sheen admitted of the texts, one of which reportedly read, "Your dad is a rock star genius ... Your mom is a [expletive] wart."
Sheen suggested testosterone cream was to blame for some of his more famous outbursts, including his "tiger blood" rant in 2011. The actor pays Richards $55,000 per month in child support, in addition to the $55,000 he sends ex-wife Brooke Mueller for their 6-year-old twin sons, Max and Bob.
"We came up with a number a long time ago [when] I had a great job and everybody was still living large," the star explained. "That's not the case right now, but there's still that expectation to still keep paying this kind of money. At some point you can't justify it, especially when there's no gratitude behind it."
Richards has yet to address Sheen's denial, but did criticize the actor's lawyer, Martin Singer, shortly after she filed the lawsuit. The 45-year-old actress chided Singer for suggesting she's greedy, tweeting, "Marty singer u being the trustee should support a mom fighting to keep it intact for the children."