WASHINGTON — President Donald Trump directly asked Ukraine’s president for a “favor” while discussing U.S. military aid to the besieged country, according to a White House memo of their July 25 phone call, suggesting a link that could be crucial to the Democrats’ fast-moving impeachment inquiry.

The details emerged as the Justice Department confirmed that the inspector general for the director of national intelligence had made a criminal referral about the call, questioning whether Trump had violated campaign finance law, but that department lawyers had determined he had not.

During the 30-minute call, Trump asked Ukrainian President Volodymyr Zelenskiy both to investigate former Vice President Joe Biden, a potential Democratic opponent in the 2020 election, and to look into CrowdStrike, a cybersecurity firm that did work for the Democrats in the 2016 election. The technology company is based in Irvine, Calif., but Trump apparently believed it operated from Ukraine.

Trump asked Zelenskiy at least five separate times on the call to work with Attorney General William Barr, putting the nation’s highest lawman directly in the House inquiry into whether Trump abused his powers and jeopardized national security by pushing a foreign government to dig up dirt on a U.S. presidential candidate.

“Whatever you can do with the attorney general would be great,” Trump told Zelenskiy after mentioning Biden several times. The Justice Department said Wednesday that Barr was unaware of Trump’s request at the time and that he did not have any contact with Ukrainian officials about the president’s request for an investigation into Biden.

Democrats quickly called for Barr to recuse himself from any related investigations.

Trump also urged Zelenskiy several times to speak to Rudolph W. Giuliani, Trump’s personal attorney. Although he is a private citizen, Giuliani has led the president’s efforts to get Ukraine to investigate Biden and his son Hunter, who sat on the board of a Ukrainian natural gas company.

“I will have Mr. Giuliani give you a call and I am also going to have Attorney General Barr call and we will get to the bottom of it,” Trump said. “I’m sure you will figure it out.”

On Wednesday, a day after House Speaker Nancy Pelosi, D-Calif., announced the start of a formal House impeachment inquiry, the White House released what it called a non-verbatim transcript, five pages compiled by note-takers in the White House Situation Room, of the July 25 call between Trump and Zelenskiy.

“There’s a lot of talk about Biden’s son, that Biden stopped the prosecution and a lot of people want to find out about that so whatever you can do with the attorney general would be great,” Trump said on the call, according to the memo. “Biden went around bragging that he stopped the prosecution — so if you can look into it. … It sounds horrible to me.”

In 2016, Vice President Biden urged Ukraine’s government at the time to fire a prosecutor whom the Obama administration and its European allies deemed soft on corruption. The prosecutor had investigated the energy company that had hired Biden’s son, but that probe had already ended by the time the vice president got involved.

No evidence has emerged to show Biden sought to help his son, and neither the former vice president nor his son has been accused of any wrongdoing.

Biden later spoke publicly about withholding U.S. financial support for Ukraine unless the prosecutor was fired, but he did not brag about stopping a prosecution of the company.

In a statement Wednesday, Biden called it “a tragedy for this country that our president put personal politics above his sacred oath” and said the attempt to involve Barr was an “attack on the core independence” of the Justice Department.

Trump argued Wednesday that his conversation with Zelenskiy was portrayed as the “call from hell,” but “it turned out to be a nothing call.”

Trump and Zelenskiy held an awkward meeting on the sidelines of the United Nations General Assembly several hours later. Zelenskiy joked that it was better meeting on television than by phone. He made clear he did not want to be involved in another country’s democratic elections.

“We had, I think, a good phone call,” Zelenskiy said. “ … Nobody pushed me.”

Zelenskiy looked at Trump with shock and confusion when Trump urged him to work more closely with Russian President Vladimir Putin, who seized Crimea in 2014 and has backed separatists fighting in eastern Ukraine. Trump also directed blame at former President Barack Obama for Russia’s invasion, leveled more accusations against Biden and rehashed old charges about Hillary Clinton’s emails.

One Ukrainian official, who requested anonymity to discuss private conversations, said Zelenskiy’s position “is not to stick his head out in either direction because no one knows who will be in the White House” after next year. “Despite his ambitions, Zelenskiy obviously is not comfortable with the idea that the outcome of the next U.S. presidential election may in some way depend on what he does or says now.”

“It’s clear that Trump is himself doing the same thing he is accusing Joe Biden of — meddling in Ukrainian justice, prosecution and internal politics,” said Alexei Arestovich, a political analyst in Kyiv.

The call memo shows Trump urged a foreign government to intervene in the 2020 election the morning after special counsel Robert S. Mueller III testified in Congress on July 24 about Russian attempts to influence the 2016 election on Trump’s behalf.

Trump acknowledged this week that he held up delivery of nearly $400 million in military and State Department aid that had been approved by a bipartisan vote in Congress to help Ukraine counter aggression from Russia. The aid was finally released this month.

Trump denied that the two-month delay in releasing the aid, which included anti-tank weapons and crucial communications systems for Ukraine’s embattled military, was meant to pressure Zelenskiy’s government to investigate Biden.

But the record of the call shows he tied the issues together. Zelenskiy brought up his desire for more U.S. military aid, saying, “we are ready to continue to cooperate for the next steps,” including the purchase of the Javelin anti-tank missiles to help fight the Russia-backed separatists.

Trump did not reply to the request for military help, asking Zelenskiy for help instead with the investigations.

“I would like you to do us a favor though,” he began. He added: “Whatever you can do, it’s very important that you do it if that’s possible.”

The White House memo shows that in addition to his interest in the Bidens, Trump was eager to find evidence that could tarnish the special counsel investigation into his 2016 campaign’s interactions with Russia.

“I would like you to find out what happened with this whole situation with Ukraine — they say Crowdstrike.”

Trump has long questioned the origins of the Russia investigation, particularly the original analysis that CrowdStrike made to determine that operatives backed by Moscow hacked Democratic National Committee computer networks.

CrowdStrike did not immediately respond to requests for comment.

Trump’s allies suspect some Ukrainian officials helped the investigation led by Mueller, who prosecuted Trump’s former campaign chairman, Paul Manafort, on charges of bank fraud, tax evasion and other crimes related to his work as a political consultant for the former Russian-backed government in Kyiv. Manafort was convicted and sentenced to 7 [1/2] years in prison.

Zelenskiy appeared eager to win Trump’s favor on the call, telling the president that he has stayed at his New York hotel and that he has adopted his “drain the swamp” slogan as a guiding philosophy.

He assured Trump that an assistant had already spoken with Giuliani “and we are hoping very much that Mr. Giuliani will be able to travel to Ukraine and we will meet once he comes to Ukraine.”

“I just wanted to assure you once again, that you have nobody but friends around us,” Zelenskiy added.

The impeachment inquiry has focused so far on Trump’s phone call, as well as a still-secret whistleblower’s complaint to the office of the director of national intelligence, and the criminal referral to the Justice Department that followed.

Barr’s office, which has supported the Trump administration’s efforts to keep the complaint under wraps, said Wednesday that no crime had been committed.

Barr’s spokeswoman, Kerri Kupec, said the intelligence community’s inspector general had cited the president’s phone call with Zelenskiy “as a potential violation of federal campaign finance law, while acknowledging that neither the inspector general nor the complainant had firsthand knowledge of the conversation.”

Kupec said the criminal division “reviewed the official record of the call and determined, based on the facts and applicable law, that there was no campaign finance violation and that no further action was warranted.”

Kupec also said Wednesday that Barr has not spoken with Trump, Giuliani or Ukrainian officials about the request for an investigation into Biden.

House Democrats said the call memo bolsters their inquiry because it shows Trump sought to pressure a foreign leader to help his reelection campaign.

Rep. Adam Schiff, D-Calif., who heads the House Intelligence Committee, said the non-verbatim transcript portrays “a classic mafia-like shakedown of a foreign leader.”

Pelosi echoed that language, saying the president was using “taxpayer money to shake down other countries for the benefit of his campaign,” she said. “Either the president does not know the weight of his words or he does not care about ethics or his constitutional responsibilities.”

Sen. Mitt Romney, R-Utah, is the only Republican in Congress who has expressed serious concern about the content of the phone memo, calling it “deeply troubling.”

“The president of the United States asks or presses the leader of a foreign country to carry out an investigation of a political nature, that’s troubling,” he said at the Atlantic Festival.

Romney — who faced Twitter backlash from the president after he went public with his concern — speculated that few Republicans are willing to speak out against the president because “there’s such enormous power associated with being the party in power.”

The whistleblower’s complaint is believed to go beyond the single phone call to include other actions undertaken by the president.

The Trump administration has promised to provide the complaint to Congress after it goes through the declassification process, which could happen by the end of the week.

The latest, and arguably most serious challenge to Trump’s presidency, has moved with remarkable speed. Details of the whistleblower’s complaint were revealed only last week, triggering a wave of new Democratic calls for impeachment proceedings.

The Mueller probe, by contrast, progressed largely in secrecy over two years, leaving many Democrats, including Pelosi, cautious over initiating an impeachment probe.

Trump’s decision to release the White House notes was unusual because such records normally are closely held to protect the confidentiality of presidential conversations with world leaders.

In previous administrations, transcripts were often produced by two intelligence officials who listened to calls with foreign leaders, said Larry Pfeiffer, who handled the process as senior director of the White House Situation Room.

Recordings were not kept, Pfeiffer said, and documents detailing the conversations were not circulated widely.

“It was a small universe,” he said.

Times staff writers Jennifer Haberkorn, Del Quentin Wilber and Sarah D. Wire contributed to this report. Times special correspondent Sergei Loiko contributed from Kyiv.