By MJ Lee, CNN National Politics Reporter

(CNN) -- President Donald Trump and his former lawyer, Michael Cohen, both made clear over the weekend that they are ready to be done with the legal drama involving adult film star Stormy Daniels.

Daniels' lawyer, Michael Avenatti, is hitting back: Not so fast.

In a new court filing on Monday, Avenatti argued: "Defendants' sudden desire to escape having to defend this action without any meaningful consequence reflects a profoundly troubling reality -- that Defendants have been shamelessly deceiving this Court and the American public for more than six months."

In the filing, Avenatti accused Trump, Cohen and others in their circle of having run a campaign to "intimidate and bully" Daniels into silence. He pleaded that "the Court cannot simply allow Defendants to exit the case without facing any true consequences or a meaningful inquiry into the truth. The public interest in continuing with this case is self-evident."

This latest move from Avenatti comes after Cohen -- followed soon after by Trump -- took action over the weekend to try to move past the Daniels saga.

Daniels alleges to have had an affair with Trump more than a decade ago. Cohen arranged a $130,000 payment to Daniels in 2016 shortly before the election, as a part of a so-called "hush agreement" to keep her quiet. Daniels launched a lawsuit earlier this year, arguing that the agreement was never valid because Trump himself had not signed it.

On Friday, Cohen's shell company, Essential Consultants, filed a document with the court agreeing to tear up the agreement with Daniels and asking her to return the money she received. In Monday's filing, Avenatti argued that Daniels shouldn't have to return the money because the "Defendants have already received the benefit of the Settlement Agreement by preventing Plaintiff from speaking prior to the 2016 election and thereby ensuring victory."

Trump, through his attorney Charles Harder, likewise moved on Saturday to get past Daniels' lawsuit, saying they would not contest Daniels' "assertion that the Settlement Agreement was never formed, or in the alternative, should be rescinded." Harder called for Daniels to "immediately dismiss" Trump from the lawsuit and requested a meeting with Avenatti if she would not agree to dismiss Trump voluntarily.

Avenatti called the moves "shenanigans" in a statement over the weekend in response to the filings from Cohen and Trump, and in a tweet, he said Trump was trying to avoid being deposed. Avenatti said in the filing on Monday that Daniels "vigorously opposes" dismissing the suit.

A status conference is scheduled for Sept. 24.