Mr Trump was said to have badgered Volodymyr Zelensky to press ahead with the probe into Joe Biden’s son, even suggesting he work with his personal lawyer, Rudy Giuliani.
The Wall Street Journal said Mr Trump made the request to his Ukrainian counterpart eight times during the phone call in July. The Washington Post also said Mr Trump made the request during the call, which took place one day after former special counsel Robert Mueller testified before Congress about Russian interference in US elections.
“He told him that he should work with [Mr. Giuliani] on Biden, and that people in Washington wanted to know” if his lawyer’s assertions that Mr Biden acted improperly as vice president were true, the Journal reported.
The revelations will add to the controversy Mr Trump has found himself in over a complaint submitted by an intelligence whistleblower that involves a conversation Mr Trump had with a foreign leader.
Earlier this month, Democrats on Capitol Hill announced they were launching investigations into efforts by Mr Trump to ask Ukraine to interfere in 2020. The Democratic chairs of the house intelligence, oversight and foreign affairs committees wrote to the White House and state department seeking records related to what they described as efforts to “manipulate the Ukrainian justice system”.
The move came after reports that Mr Giuliani, the former New York mayor who has been advising Mr Trump on legal matters, has been pressuring Mr Zelensky to open proceedings into claims made by Republicans that Mr Biden acted unfairly to help his son, Hunter, in business dealings.
Mr Giuliani had been liaising with prosecutors in Kiev appointed by Mr Zelensky’s predecessors, to look into the company Hunter Biden worked for, and the oligarch who owned it.
On Thursday night Mr Giuliani insisted to CNN that he didn’t ask Ukrainian officials to investigate Mr Biden, but 30 seconds later said “of course” he did.
On Friday, before the revelations in Journal, Mr Trump claimed the whistleblower was “partisan”, while also insisting he had done nothing wrong.
Speaking to reporters in the Oval Office on Friday morning, Mr Trump said: “I can say it was a totally appropriate conversation.”
He added: “It was actually a beautiful conversation.”
The complaint against the president emerged this week but is still shrouded in mystery. Apparently made by a US intelligence officer who was listening in to a call between Mr Trump and a world leader, it was classed as “serious” and “urgent” by the intelligence watchdog.
However, the acting director of national intelligence has so far refused demands from congress to reveal the exact nature of the complaint.
The Trump administration has denied links between a $250m (£200m) aid payment to Ukraine and the provision of negative information about Mr Biden and his son Hunter’s business dealings in the east European country.
Mr Trump insisted the person who made the complaint against him was “partisan” before admitting he did not know their identity.
He said: “We don’t know the identity of the whistleblower, we just know that it was a partisan person, meaning they come from a different party,” adding that he “fights so hard for this country”.
When asked again if he knew anything about the whistleblower, the president, visibly annoyed, fired back: “You’re supposed to be the media, figure it out.” And in response to a question over whether the complaint involved Ukraine, he said: “I really don’t know.”
He said he was under no obligation to explain what he discussed with Mr Zelensky in one of several phone conversations with world leaders made in the days before the complaint was filed, saying: “It doesn’t matter what I discussed, but I will say this: somebody ought to look into Joe Biden’s statement, because it was disgraceful, where he talked about billions of dollars that he’s not giving to a certain country unless a certain prosecutor is taken off the case.
“So, somebody ought to look into that. And you wouldn’t, because he’s a Democrat. And the ‘fake news’ doesn’t look into things like that. It’s a disgrace.”
Mr Trump will meet Mr Zelensky at the United Nations general assembly in New York next week where, a US administration official told reporters, he will congratulate him on his anti-corruption efforts.
Adam Schiff, the Democratic chair of the House intelligence committee, has threatened to sue the administration if intelligence officials do not share the complaint. He said it was unprecedented for the acting director of national intelligence, Joseph Maguire, to refuse to share the briefing with congress.
“We cannot get an answer to the question about whether the White House is also involved in preventing this information from coming to congress,” Mr Schiff said. “We’re determined to do everything we can to determine what this urgent concern is to make sure that the national security is protected.”
Democratic congressman Jim Himes, who serves on the intelligence committee, told CNN he would not be surprised if Mr Trump was indeed having an “inappropriate” conversation with a foreign leader, but was concerned by the news that the complaint involved a promise. “What would make it corrupt or illegal,” he said, is that promise.
House speaker Nancy Pelosi said Mr Trump faced “serious repercussions” if the reports were accurate, saying the complaint raises “grave, urgent concerns for our national security”.
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