"My client was physically threatened to stay silent about what she knew about Donald Trump", he said on CNN.
Under the nondisclosure agreement, Daniels, whose legal name is Stephanie Clifford, could be subjected to a $1 million penalty each time the deal was broken. Until now, Trump has tried to keep his distance from the Daniels saga, instead leaving it to his personal lawyer, Michael Cohen, to deal with.
Mr Avenatti has filed a lawsuit in Los Angeles claiming Mr Trump never signed the nondisclosure agreement, rendering it null and void. He did not explain why he made the payment or say whether Trump was aware of it.
The latest turn in the dispute trails what promises to be an explosive CBS 60 Minutes' interview with Clifford, scheduled for broadcast next Sunday.
An accusation the Trump team denies. She however violated the non -disclosure agreement claiming that Trump did not sign it and that made freed her from the obligation.
"I'll give you the same answer", Mr Avenatti told host Mika Brzezinski.
"We're still in the process of vetting these allegations", he said.
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Asked about Mr. Avenatti's allegation relating to threats on Friday, the president's press secretary, Sarah Huckabee Sanders, said she had "no knowledge" about it, but "obviously we take the safety and security of any person seriously".
Attorney Charles Harder - best known for representing Hulk Hogan in a successful lawsuit against Gawker, which resulted in its bankruptcy - is handling the legal case against Daniels on the president's behalf.
Stormy Daniels" lawyer Michael Avenatti called the $20 million lawsuit from President Donald Trump an attempt to "intimidate' Stormy and his filing to move the lawsuit to federal court an attempt to get the lawsuit settled behind closed doors.
Two of the women appear to have signed nondisclosure agreements, Avenatti said. The Wall Street Journal reported that a Trump Organization attorney was listed on confidential arbitration documents that included the restraining order against Daniels.
Mr Cohen has previously said he paid Ms Clifford $US130,000 of his own money during the 2016 presidential campaign.
In addition to Clifford, six women have contacted Avenatti with similar stories, he said. But her case came back into public view in October 2016, as she became concerned that the $130,000 she was promised would not come through.
In its motion, Mr. Trump's legal team indicates that it considers her liable for $20 million, for 20 breaches it did not detail.