The feud between Denise Richards and Charlie Sheen that reignited this week is getting even uglier.

Richards, 37 - in NYC to promote her new E! reality show — is now claiming that Sheen, 42, sent her vulgar text messages attacking her father and mother, who recently died of cancer.

"Last week, I sent Charlie a text message asking him if he's going to Family Day [for daughter Sam's school] and letting him know Sam was sick with a cold," Richards told the New York Post.

"His response was, 'I hope you and your worthless retarded father get cancer and join your stupid mom. Rot in hell you [bleeping] whore,'" Richards claims. "My mom died of cancer. This is what I deal with on a weekly basis.

"He missed Dad's day at the school, and my father had to go in his place. And this is how he talks to me?"

Their ongoing war resumed Wednesday when Richards claimed on the Today show that Sheen faked e-mails from her, asking Sheen's fiancee, Brooke Mueller, for his sperm.

"I don't want Charlie's prostitute-tranny-infested sperm," Richards tells the Post. "I have two beautiful kids. We'll leave it at that.

"I am so over him," she says. "He's the one who can't move on. He's disgusting, and he's hit an all-time low."

Sheen's rep fired back: "Denise seems to be denying the existence of [the] e-mail. This goes beyond a he-said-she-said. We have an offer from a [live] TV show. They will bring a computer expert to diagnose the e-mail and to verify it was sent by her e-mail address and to verify it was neither altered nor edited. Computer DNA — it is conclusive.

"The only time Charlie has spoken on TV about her, they were sound bites at red-carpet visits or during set visits," the rep said. "He has not gone on multiple TV shows this week."