An adult film actress who said she had sex with US President Donald Trump has offered to return the 130,000 dollars (£93,500) she was paid for agreeing not to discuss their alleged relationship.

An attorney for Stormy Daniels, whose real name is Stephanie Clifford, sent a letter to Mr Trump’s lawyer on Monday saying she would wire the money to Mr Trump if she could speak openly about their relationship.

The letter was sent by Clifford’s lawyer to Mr Trump’s attorney, Michael Cohen and his attorney, Lawrence Rosen.

The letter said that if the offer was accepted, the non-disclosure agreement would be “deemed null and void”.

TrumpThe White House is yet to comment (Carolyn Kaster/AP)

Clifford’s lawyer, Michael Avenatti, said Mr Trump and Mr Cohen should accept the proposal and allow Clifford to tell her side of the story.

“Mr Cohen and the president should accept this proposal and allow Ms Clifford to tell her side,” Mr Avenatti said. “The American people can then decide who was telling the truth.”

The offer is valid until Tuesday afternoon, the letter said.

Mr Cohen and Mr Rosen did not immediately respond Monday to requests for comment.

Clifford filed a lawsuit in Los Angeles last week that sought to invalidate the agreement so she could “set the record straight”.

The lawsuit claimed the “hush agreement” that was signed days before the 2016 presidential election is legally invalid because it was only signed by Clifford and Mr Cohen and not by Mr Trump. It refers to Mr Trump as David Dennison and Clifford as Peggy Peterson, but an attached exhibit details their true identities.

The Dallas Morning News reported on Monday that Texas officials are investigating whether a notary properly witnessed the non-disclosure agreement. The officials sent a letter to notary Erica Jackson notifying her that there was “good cause” to take action against her notary commission.

Her stamp appears on the document but she did not sign or date it, and she did not provide a certificate of whose signature she was witnessing, officials said.

White House Press Secretary Sarah Sanders said last week that Mr Trump has made it clear that none of the allegations are true. The White House did not respond to a request for comment on Monday.

Mr Cohen has also denied there was ever an affair and said he paid the 130,000 dollars out of his pocket. He said neither the Trump Organisation nor the Trump campaign was a party to the transaction with Clifford.

“Neither reimbursed me for the payment, either directly or indirectly,” he said.

Clifford alleged in the lawsuit that Mr Trump was aware of the negotiations.

Also on Monday, the advocacy group Common Cause named Mr Trump and Mr Cohen in amended complaints to the Federal Election Commission and Justice Department that alleged the payment to Clifford violated campaign finance laws.

The complaints allege Mr Cohen was an agent of then-candidate Mr Trump and should be considered a campaign expenditure and in-kind contribution.

“Emerging details appear to directly link President Trump to the hush money payments to the adult film star expanding the list of apparent violations,” said Paul S Ryan, the group’s vice president for policy and litigation.

“Hush money may be commonplace in some businesses, but when it is spent to influence a federal election it must be disclosed – without exception.”