US President Donald Trump's personal lawyer has told the New York Times that he paid $130,000 of his own money to a porn star who once said she had an affair with Mr Trump.

Michael Cohen said he was not reimbursed for the payment to the actress, whose real name is Stephanie Clifford and goes by Stormy Daniels, the newspaper said.

Mr Cohen said the payment was legal, but declined to give details as to why he made it.

"Neither the Trump Organization nor the Trump campaign was a party to the transaction with Ms Clifford, and neither reimbursed me for the payment, either directly or indirectly," Mr Cohen said, according to the New York Times article.

"The payment to Ms Clifford was lawful, and was not a campaign contribution or a campaign expenditure by anyone."

US media reports have said the payment was made one month before the November 2016 election to keep the liaison quiet.

Mr Trump was a private citizen when the 2006 sexual encounter with Ms Clifford allegedly took place.

He was married at the time and his wife, Melania, had given birth to their son less than four months earlier.

The payment was first reported last month by the Wall Street Journal.

Mr Trump, through his lawyers, and Ms Clifford, 38, have both denied anything ever went on between them.

But In Touch magazine published a 2011 interview with Ms Daniels last month in which she spoke at length and in detail about their relationship.