A law firm representing President Donald Trump and the corporation owned by Donald Trump's personal lawyer, Michael Cohen, have claimed porn star Stormy Daniels could owe more than $20m (£14.3m) in damages for violating a nondisclosure agreement that prevented her speaking about an alleged affair with the US President.

The court document alleges Ms Daniels – real name Stephanie Clifford – is guilty of at least 20 violations of the agreement's confidentiality clause and could face a $1m (£700,000) penalty for each violation.

Ms Daniels, who filed a lawsuit against Mr Trump earlier this month, claims the nondisclosure agreement is void because Mr Trump did not sign it himself. Instead it was signed by a lawyer for the Trump Organisation.

The alleged affair between Ms Daniels and Mr Trump is said to have occurred in 2006, less than four months after first lady Melania Trump gave birth to the couple’s son, Barron.

But it was only in January this year after rumours of the affair resurfaced that In Touch magazine published an interview with Ms Daniels from 2011, in which she gave a detailed account of the alleged relationship. Mr Trump denies the affair.

Friday's claim against the actress was made in a court filing in California by representatives of the Blakely Law Group.

Michael Avenatti, Ms Daniel’s lawyer, described the filing as “yet another bullying tactic from the president and Mr Cohen,” referring to Mr Trump's personal lawyer, Michael Cohen, whose company is also represented by the Blakely Law Group.

“The fact that a sitting president is pursuing over $20m in bogus 'damages' against a private citizen, who is only trying to tell the public what really happened, is remarkable,” Mr Avenatti wrote on Twitter. “Likely unprecedented in our history."

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Mr Cohen has already been involved in multiple legal efforts to silence Ms Daniels.

The lawyer claims he paid the actress $130,000 to keep quiet about the alleged affair in the run-up to the presidential election. He has not said whether Mr Trump was aware of the payment.

Mr Cohen also obtained a restraining order against Ms Daniels last month in a further attempt to prevent her from speaking out.

The court filing also calls for a lawsuit brought by Ms Daniels seeking to invalidate the agreement to be moved from a county to a federal court, which Mr Avenatti describes as a further attempt to hide “the truth from the public”.

He argues that the move would increase the chances that the case would be decided in private arbitration.

Earlier on Friday in an interview with CNN, Mr Avenatti claimed his client had been “physically threatened to stay silent” about what she knew about Mr Trump, but did not provide any details of the allegations.

He instead plugged an upcoming interview Ms Daniels has given to CBS’s “60 Minutes”, saying his client would provide “very specific details about what happened here” and leave the American people with “little to no doubt that this woman is credible”.