WASHINGTON — President Trump urged the president of Ukraine to contact Attorney General William P. Barr about opening a potential corruption investigation connected to former Vice President Joseph R. Biden Jr., according to the reconstruction of a July phone call at the center of accusations that Mr. Trump pressured a foreign leader to find dirt on a political rival.
“I would like you to do us a favor,” Mr. Trump said in response to President Volodymyr Zelensky of Ukraine raising the prospect of acquiring military equipment from the United States. Noting that the United States had “done a lot for Ukraine,” Mr. Trump also asked for another inquiry: that the Ukrainians examine an unsubstantiated theory about stolen Democratic emails.
“So whatever you can do with the attorney general would be great,” the president told Mr. Zelensky, who later agreed to have the country’s new top prosecutor conduct the investigations Mr. Trump wanted.
“The next prosecutor general will be 100 percent my person, my candidate,” Mr. Zelensky assured the president. “He or she will look into the situation.”
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After a whistle-blower raised concerns about Mr. Trump’s dealings with Ukraine, the director of national intelligence and the inspector general for the intelligence community each referred the complaint for a possible criminal investigation into the president’s actions, according to a Justice Department official.
The five-page “memorandum of telephone conversation” distributed by the White House includes a cautionary note indicating that it was “not a verbatim transcript” but instead was based on “notes and recollections of Situation Room Duty officers” and national security staff. But senior administration officials said voice recognition software was used in preparing the document which included long, direct quotations.
The department’s criminal division reviewed the matters and concluded that there was no basis for a criminal investigation into Mr. Trump’s behavior. Law enforcement officials determined that the reconstructed transcript of the call did not show that Mr. Trump had violated campaign finance laws by soliciting from a foreign national a contribution, donation or thing of value.
During the call, Mr. Trump told Mr. Zelensky that he should be in touch with both Mr. Barr and the president’s personal lawyer Rudolph W. Giuliani, according to the document, known among government officials as a “memcon.”
“There is a lot of talk about Biden’s son, that Biden stopped the prosecution, and a lot of people want to find out about that,” Mr. Trump said to Mr. Zelensky during the call, according to the memorandum.
The Justice Department said Wednesday that Mr. Barr was unaware that Mr. Trump had told Mr. Zelensky that he would contact him. The department said that Mr. Barr has never spoken with Mr. Trump about working with Ukraine to investigate anything related to the Bidens and that he has never spoken with Mr. Giuliani about “anything related to Ukraine.”
Though rooting out widespread corruption in Ukraine has long been an American foreign policy goal, Mr. Trump referenced Mr. Biden, a leading Democratic candidate for president, during the call. Mr. Trump and Mr. Giuliani have long pushed for Ukrainian officials to examine whether there was any improper overlap between Mr. Biden’s dealings with Ukraine while in office and his son’s position on the board of a Ukrainian energy company.
But Mr. Trump’s suggestion that American law enforcement be directly involved and in contact with Ukraine’s government marks the first evidence that the president personally sought to harness the power of the United States government to further a politically motivated investigation.
Mr. Trump specifically asked his Ukrainian counterpart to come to the aid of the United States by looking into the unsubstantiated theory pushed by Mr. Giuliani holding that Ukrainians had some role in the emails stolen from the Democratic National Committee.
“I would like to have the attorney general call you or your people and I would like you to get to the bottom of that,” Mr. Trump said on the call, also referencing Robert S. Mueller III, the special counsel who investigated Russia’s election sabotage. “Whatever you can do, it’s very important that you do it, if that’s possible.”
Mr. Trump’s allies argue that he was not exerting improper pressure on Mr. Zelensky, but mentioned Mr. Barr because the Justice Department was already reviewing the origins of the inquiry into Russia’s 2016 election meddling.
The president’s mentions of Mr. Barr and Mr. Giuliani were the most striking part of a half-hour conversation in which the two men discussed a series of issues. But several times, Mr. Trump steered the conversation back to Mr. Barr, Mr. Giuliani and Mr. Biden.
There was no explicit reference to the $391 million in foreign aid that Mr. Trump had told Mick Mulvaney, the acting White House chief of staff, to put a hold on several days before the call took place.
Mr. Giuliani, who has pursued the allegations against Mr. Biden and his son since January, said Mr. Trump would have been shirking his duty to enforce the laws of the United States had he not asked the Ukrainian government to pursue the allegations against Mr. Biden and his son.
Regardless of the fact that Mr. Biden is Mr. Trump’s political opponent, he said, allegations against Mr. Biden required investigation, and only Mr. Trump had the status to ask the Ukrainian president to open an inquiry.
“The only person that can raise that is the president of the United States,” he said. “The president of Ukraine is not going to take a call from the head of the F.B.I.,” he said. “If you are asking me if it is proper to do it, of course it is. It is his job to make sure that the laws are faithfully executed. Asking him to investigate Biden is far different than threatening him.”
The details of the call — which were first revealed by a whistle-blower who works in the intelligence community — prompted Democrats on Tuesday to formally open an impeachment inquiry, accusing Mr. Trump of betraying his country by pressuring a foreign leader to dig up dirt on Mr. Biden.
But until Wednesday, lawmakers had not yet seen the reconstruction of the call, which documents the 30-minute call and includes banter about Mr. Zelensky staying at the Trump Hotel and the two men comparing which of their airplanes is better.
Officials said Mr. Zelensky’s statements were translated into English by an American official. In three of Mr. Trump’s passages, the document includes an ellipsis indicating that part of the president’s statement may be missing, though it is unclear how much was not included in the memorandum. Administration officials said the ellipses indicate that Mr. Trump’s voice trailed off or there was something inaudible.
In the days before the memorandum of conversation was released, news reports revealed that Mr. Trump used the call in July to pressure Mr. Zelensky for an investigation about Mr. Biden’s actions on behalf of his son Hunter Biden’s work with a business in Ukraine.
That followed repeated efforts over the past several months by Mr. Giuliani to urge the Ukrainians to start an investigation into Mr. Biden.
Over the weekend, Mr. Trump publicly acknowledged that he discussed the former vice president with Mr. Zelensky, even as he angrily railed against what he called another “witch hunt” and insisted that his conversation with the Ukrainian president was perfectly appropriate.