Trump disparaged the practice in an interview a day after learning that his ex-attorney MichaelCohen had copped to eight crimes, including two that Cohen says he committed at the direction of the president, to cut down on his expected amount of jail time.
Mr Giuliani, Mr Trump's personal counsel, was speaking during a golf trip to Scotland.
■Stormy Daniels, whose real name is Stephanie Clifford, said she had a brief affair with Trump.
As the legal net closed in on Trump, he renewed attacks on his own Attorney General Jeff Sessions, in an apparent attempt to have him squash awkward investigations that could endanger the president.
He added: "The reality is that the president has completely been vindicated by the whole Cohen incident". He expressed his views during a sit-down interview with Fox News. He's worth millions and has been taped in the past threatening reporters, once telling a Daily Beast journalist to tread "very f-- lightly because what I'm going to do to you is going to be f-- disgusting".
"A subpoena has been issued to Michael Cohen for relevant information in light of the public disclosures made yesterday", said Tax Department spokesperson John Gazzale in a statement. Trump has denied having sex with the women.
The problem was the hush payments to former Playboy model Karen McDougal and porn actress Stormy Daniels.
"Fake News reporting, a complete fabrication, that I am concerned about the meeting my wonderful son, Donald, had in Trump Tower", the president wrote.
Trump has lashed out repeatedly in the past at Sessions, the Alabama Republican who was the first senator to endorse the celebrity businessman but then recused himself shortly after taking office from the special counsel investigation that led to the criminal cases and is still underway into possible collusion between Russian Federation and the Trump campaign.
While the President was aware for weeks of the possible damage Cohen could do in his dealings with federal prosecutors, Trump did not know until Tuesday afternoon that he would be so explicitly implicated in the campaign finance charges.
Trump himself has opined on this possibility in recent days, telling Fox News in an interview that he doesn't "know how you can impeach somebody who's done a great job".
"But it leads him closer to ultimate impeachment proceedings, particularly if the Democrats take back the House", he said. While Giuliani had warned of a people's uprising if Trump is impeached, Trump himself has said there will be a financial meltdown if that happens.
Here are five questions (and answers) about President Trump and the legal problems with those hush payments. "If Trump is either dangling a pardon or giving a pardon in order to prevent Manafort from giving truthful testimony to Mueller, that's obstruction of justice - and it doesn't change it that he's the president of the United States".