"I was about to push the button on a really snarky tweet. Then I saw my son, daughter, and wife and I deleted it," Kutcher, 41, tweeted on Tuesday night.
He followed with, "Life is good -Larry Kutcher." An hour later, he posted his phone number, writing, "For the truth, text me." A follower who claimed to have texted the number alleged that it was a data grab.
Moore, 56, accused Kutcher of infidelity during their relationship, which she says was sparked by them having threesomes with other women.
"He expressed something that was of a fantasy and it was in my efforts to want to please and be what I thought he wanted," she said.
"It was a misguided sense of not really wanting to look at the harder question or maybe what was really missing. Or, in my case, because I really felt like I had created an addiction to him... I never had that kind of attachment," she admitted.
According to The New York Times, Moore writes in her forthcoming memoir “Inside Out” that she blamed herself for miscarrying her and Kutcher's child at six months. Moore also reveals that she began abusing Vicodin and alcohol to cope, which ultimately spelled doom for the relationship.
The actress previously said she spoke with Kutcher, who's now married to and shares two kids with Mila Kunis, about the claims in her book.
Fox News' Julius Young and Jessica Napoli contributed to this report.