Trump's lawyers filed two motions Friday in U.S. District Court in California in a public legal fight that Clifford, whose stage name is Stormy Daniels, started earlier this month.
Daniels says Cohen paid her $130,000 12 days before the 2016 election in exchange for her silence about a year-long affair she had with Trump in 2006.
Avenatti seemed unfazed by the efforts Harder and Essential Consultants to move the lawsuit from state to federal court. Trump may be hoping that his chances of keeping the dispute in arbitration and out of public view are better before a federal judge than a state one.
Until now, Trump has kept his distance from the legal wrangling, leaving it to his personal lawyer, Michael Cohen, to take the lead in refuting Clifford's claims. One of the motions is filed on Trump's behalf and mentions him directly.
Earlier on Friday, Avenatti told MSNBC and CNN that Daniels had been physically threatened and warned to remain silent about her relationship with Trump.
It's a tactic that's had mixed results since he chose to run for president. She taped an interview with CBS News' 60 Minutes program last week that has yet to be broadcast.
"The fact that a sitting president is pursuing over $20 million in bogus "damages" against a private citizen, who is only trying to tell the public what really happened, is truly remarkable - likely unprecedented in our history".
They allege that Daniels as many as 20 times violated the confidentiality provisions of a settlement agreement in which Cohen paid the adult film actress $130,000 through a private LLC. He added, "We are not going away, and we will not be intimidated by these threats".
In a statement late Wednesday, the Trump Organization said Martin worked on the filing in her "individual capacity" and the company "has had no involvement in the matter".
Stormy Daniels has expressed her desire to fully tell her encounters with Donald Trump.
I need funds to pay for: attorneys' fees; out-of-pocket costs associated with the lawsuit, arbitration, and my right to speak openly; security expenses; and damages that may be awarded against me if I speak out and ultimately lose to Mr. Trump and Mr. Cohen.
Clifford could face a $1 million penalty if she breaks the non-disclosure agreement.
Harder appeared to be seeking to answer a key challenge from Ms. Clifford's lawyer, Mr. Avenatti, that in failing to sign the original deal, Mr. Trump was not bound by it. New documents show a to.