After a whistleblower alleged Mr Trump abused his power to “solicit interference from a foreign country” in his 2020 re-election bid by urging Ukraine's president to investigate his Democratic rival Joe Biden and his son Hunter, the former mayor of New York insisted he would stand by his leader.
Washington has been rocked by the complaint, which reportedly came from a senior member of the US Intelligence Community.
They claimed that White House lawyers “locked down” evidence and transcripts of the phone call between Mr Trump and Ukrainian president Volodymyr Zelensky.
Days after ordering a freeze to some military assistance for Ukraine, on 25 July, the US president pressed Mr Zelensky to work with Mr Giuliani, his personal lawyer and US attorney general William Barr to investigate Mr Biden.
Hunter Biden was a board member Burisma, a Ukrainian natual gas company and Mr Trump has alleged that Mr Biden pressed for the sacking of Ukrainian prosecutor Viktor Shokin in 2016 to protect the business.
While serving as vice president and leading the Obama administration’s diplomatic dealings with Kiev, Mr Biden did call for Mr Shokin to be removed from his post.
He also threatened to withhold $1bn (£813m) in aid to Ukraine.
But he was one of a number of western officials who saw Mr Shokin as a hindrance to anti-corruption investigations and there is no suggestion of impropriety on behalf of either Mr Biden or his son.
After details of the whistleblower's complaint emerged, Mr Trump's Democratic rivals launched an official impeachment inquiry – a rare two-stage political process which could ultimately see him removed from office.
He is only the fourth American president in history to face the move.
The complaint stated that about a week after the 25 July call made by Mr Trump, Mr Giuliani travelled to Madrid, Spain, to follow up on the conversation with Mr Zelensky’s aide, Andriy Yermak.
It also cites published reports of meetings Mr Giuliani held with Ukraine’s chief prosecutor in New York in January and then in the Polish capital Warsaw the following month.
He also held a phone call with the prosecutor’s predecessor late last year.
Mr Giuliani has insisted that what he did was “perfectly lawful, perfectly legal”.
He told Sky News that he was put in touch with Mr Yermak by Mr Trump’s Ukraine envoy Kurt Volker, who resigned on Friday after he was accused of trying to “contain the damage” from efforts by Mr Giuliani, to press Mr Zelensky to investigate.
Asked whether he would testify before Congress, he said: “Well there’s a lot of problems with that. I mean would I like to testify and tell my story. Sure. I’ve been telling it. All the time. In fact, you know my story.”
However, Mr Giuliani said there were things he could not testify as a lawyer. In a separate interview he told CNN he would not do so without consulting Mr Trump first.
His comments came as one former White House official told the US broadcaster that memos of calls with Saudi Arabia’s Crown Prince Mohammed bin Salman and Russia’s Vladimir Putin were also among those restricted – a practice that began after leaks in 2017.
Agencies contributed to this report.
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