Donald Trump called Stormy Daniels “Horseface” on Tuesday, and hinted at further legal action against her, as the feud between the president and the porn star swelled back into public view.

The adult film actor and director returned fire, calling the president “Tiny”. Her lawyer, Michael Avenatti, said Trump was a misogynist.

Daniels claims she had a sexual relationship with Trump in 2006. Earlier this month, as first reported by the Guardian, she released a book in which she discussed the alleged affair, describing Trump’s genitalia in detail. Trump denies the allegation.

In California on Monday afternoon, a federal judge threw out out a defamation lawsuit Daniels filed against Trump, one of a series of legal actions between the two in New York and Los Angeles.

On Tuesday morning Trump was busy, tweeting from the White House on themes such as the economy, Saudi Arabia and his quarrel with Senator Elizabeth Warren. Then he launched his fresh attack on Daniels.

Trump tweeted: “‘Federal Judge throws out Stormy Daniels lawsuit versus Trump. Trump is entitled to full legal fees’.’ @FoxNews. Great, now I can go after Horseface and her third rate lawyer in the Great State of Texas.”

Avenatti is an outspoken critic of the president who has touted himself as a possible candidate for the Democratic presidential nomination. After Trump called his client “Horseface”, the lawyer retweeted the post with a comment: “You are a disgusting misogynist and an embarrassment to the United States.”

Daniels tweeted: “Ladies and Gentlemen, may I present your president. In addition to his … umm … shortcomings, he has demonstrated his incompetence, hatred of women and lack of self control on Twitter AGAIN! And perhaps a penchant for bestiality. Game on, Tiny.”

In his reference to “going after” Daniels in Texas, Trump appeared to be alluding to the fact Daniels, a keen horse rider, lives near Dallas. In excerpts of an interview with Fox News released on Tuesday afternoon, Trump said Avenatti and Daniels “have to pay me a lot of legal fees … based on Texas law, where the legal fees are nice and plentiful”.

Daniels has said that in 2011, after she agreed to talk about her experience with Trump, a man approached her in a Las Vegas parking lot and threatened her. She released a sketch of the man. In the dismissed California lawsuit, Daniels claimed a tweet in which Trump said she fabricated the parking lot encounter had defamed her, making her out to be a liar.

The judge said the tweet was protected by free speech laws as “rhetorical hyperbole”.

Daniels has also sued over a non-disclosure agreement (NDA) connected to a $130,000 payment made to her in 2016, relating to the alleged encounter with Trump. She is seeking to be released from the NDA, which she signed but Trump did not.

On Tuesday, Trump tweeted: “She will confirm the letter she signed! She knows nothing about me, a total con!”

Avenatti continued: “Tens of millions of Americans are tired of your fraud, lies, and corruption. They are equally tired of your attacks on women.”

He added: “Don’t mess with Stormy Daniels.”

In an interview with The Associated Press on Tuesday, Trump did not back down from derisively nicknaming Daniels “horseface” hours earlier. He said “you can take it any way you want,” when asked if it was appropriate to insult a woman’s appearance.