The lawyer, Robert Costello, said Mr Giuliani, who is Mr Trump’s personal attorney, phoned the president “at my insistence” earlier this week to say he was not serious when he told a reporter he had “insurance” if used as a scapegoat in the Ukraine scandal.
Mr Trump is facing the prospect of an impeachment trial over attempts by him and his associates – including Mr Giuliani – to pressure the Ukrainian leadership into announcing an investigation into Joe Biden, a possible presidential contender in 2020.
“He shouldn’t joke, he is not a funny guy. I told him, ‘Ten thousand comedians are out of work, and you make a joke. It doesn’t work that way’,” Mr Costello told Reuters.
Mr Giuliani has said that he was being sarcastic when he made the comments. Mr Trump, too, brushed them off, telling reporters in the Oval Office this week that “Rudy is a great guy”.
The White House declined to comment on Mr Costello’s remarks.
Following reports senior Republicans, in a bid to protect Mr Trump, were considering blaming Giuliani for the White House outreach to Ukraine, The Guardian asked the former New York mayor if he was concerned about being “thrown under the bus”.
“I’m not, but I do have very, very good insurance, so if he does, all my hospital bills will be paid,” Mr Giuliani replied.
The report said he spoke with a slight laugh in his voice. It also said Mr Costello interjected into the interview by saying, “He’s joking”.
Mr Giuliani has emerged as a central figure in the Democratic-led impeachment inquiry against Mr Trump, who is accused of abusing his office for personal political gain by pressing Ukraine to investigate Mr Biden and his son, Hunter, a former board member of a Ukrainian energy company.
Current and former US officials have testified at the inquiry that Mr Giuliani carried out a shadow foreign policy in Ukraine and that it became clear to them a White House meeting between Ukrainian president Volodymyr Zelensky and Mr Trump as well as a phone call between the two leaders was contingent on Ukraine carrying out Mr Trump’s wishes.
Mr Trump, in an interview with former Fox News host Bill O’Reilly on Tuesday, sought to distance himself from Mr Giuliani’s activities on Ukraine, saying he had not directed him to work on Ukraine matters.
“No, I didn’t direct him, but he is a warrior,” Mr Trump told Mr O’Reilly, adding Mr Giuliani “possibly saw something” and “he’s done work in Ukraine for years”.
US ambassador to the European Union, Gordon Sondland, testified that Mr Trump directed him, energy secretary Rick Perry, and former Ukraine special envoy Kurt Volker to work closely with Mr Giuliani on Ukraine matters, a request that he viewed with alarm as Mr Giuliani was a private citizen.
Additional reporting by Reuters