Daniels'attorney Michael Avenatti called Trump a"disgusting misogynist"and an"embarrassment to the United States"in response.
The tweets came after a US federal judge dismissed a lawsuit from Daniels in which she claimed that Trump defamed her when he suggested her allegation that she was threatened to stay quiet about their relationship was a lie.
Daniels' libel lawsuit was over a tweet by Trump accusing her of "a total con job".
The judge said the President was engaging in free speech.
The adult film star,whose real name is Stephanie Clifford,claimed she was threatened by an unknown man in a Las Vegas parking lot in 2011 for agreeing to cooperate with a magazine article about a tryst she says she had with Trump in 2006. After her lawyer released a composite sketch of the man,Trump accused Clifford in an April tweet of"a total con job'concerning a"non-existent man."