A lawyer for Daniels, whose real name is Stephanie Clifford, confirmed the statement was authentic but didn't offer any further details.
The statement comes at a curious time for Clifford, who is scheduled to appear following the president's State of the Union address on ABC's "Jimmy Kimmel Live!"
In recent weeks she has changed production companies, given a television interview and promoted strip club appearances with a risque play on Trump's "Make America Great Again" campaign slogan.
Clifford's allegation, first made in 2011 and then again a month before the election, went mostly unnoticed until The Wall Street Journal reported earlier this month that Cohen brokered a USD 130,000 payment to Clifford to keep her from publicly discussing it.
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A week after that report, In Touch magazine printed a 5,000-word interview it conducted with Clifford in 2011 but never published after Cohen threatened the tabloid with a lawsuit, The Associated Press has previously reported.
In that interview, Clifford described a single sexual encounter with Trump in 2006, when he was recently married to his third wife, Melania, as well as a subsequent years-long relationship with the reality TV star. The magazine said it corroborated her account with friends and said she passed a lie detector test.
Neither Cohen nor Clifford has addressed whether she was paid USD 130,000, or if so, why.
A publicist didn't respond to questions about the statement today.