The Trump administration has released the much-anticipated transcript summary of President Trump's phone call with Ukraine President Volodymyr Zelensky, after Mr. Trump authorized publishing the transcript. A memo summarizing the call shows that the president urged Zelensky to probe Joe Biden and his son, Hunter Biden, who sat on the board of a Ukrainian natural gas company.

The memorandum released by the Justice Department is not, according to the administration, a verbatim transcript. The text, according to a footnote, is the record of the notes and recollections of the officers and National Security Council policy staff "assigned to listen and memorialize the conversation in written form."

According to the call summary, Mr. Trump told Zelensky, "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. Biden went around bragging that he stopped the prosecution so if you can look into it...It sounds horrible to me."

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The president and his personal attorney Rudy Giuliani have accused Biden of acting inappropriately in March 2016, when during a visit to Kiev, he threatened to withhold U.S. funding unless Ukraine ousted then-prosecutor general Viktor Shokin, whom Western leaders and the U.S. had denounced as corrupt. The Ukrainian parliament voted overwhelmingly to remove Shokin in 2016. While he had opened an investigation into the Ukrainian natural gas company whose board members included Hunter Biden, it was dormant by the time he was ousted.

During the call, Mr. Trump referred to Shokin in positive terms. "I heard you had a prosecutor who was very good and he was shut down and that's really unfair," he said. "A lot of people are talking about that, the way they shut your very good prosecutor down and you had some very bad people involved."

The president's call with Zelensky took place a day after Robert Mueller testified before Congress about the Russia investigation and about whether Mr. Trump had obstructed justice, and the topic of the Russia probe also came up during the call. After Zelensky expressed his gratitude to Mr. Trump for the aid Ukraine received from the U.S., he said Ukraine was "ready to continue to cooperate for the next steps" in enforcing sanctions against Russia. "Specifically," Zelensky said, "we are almost ready to buy more Javelins (missiles) from the United States."

Mr. Trump responds, "I would like you to do us a favor though because our country has been through a lot and Ukraine knows a lot about it. I would like you to find out what happened with this whole situation with Ukraine, they say Crowdstrike ... I guess you have one of your wealthy people... The server, they say Ukraine has it."

CrowdStrike is a cyber security firm that in 2016 was called by the Democratic National Committee when it noticed unusual activity. It helped investigate Russian interference in the 2016 election and discovered two separate hacking groups connected to the Russian government had breached the DNC's network.

Mr. Trump told Zelensky his personal lawyer, Rudy Giuliani and Attorney General William Barr would be calling Zelensky to "get to the bottom of it." Mr. Trump be traveling to Ukraine. Zelensky said he would meet with Giuliani when he visited.

Zelensky also pledged that his new prosecutor would look into the case, and he asked for additional information.

At the United Nations, Wednesday, Mr. Trump remarked, "I will say that we do a lot for Ukraine. We spend a lot of effort and a lot of time." Until earlier this month, Mr. Trump had temporarily frozen $391 million in aid to Ukraine. Ultimately, the White House released the funds to Ukraine in September, after withholding the aid for about two months.

Read the full memorandum released by the Justice Department:

Download PDF version of this memorandum.

Mr. Trump, under pressure to release the transcript, had already confirmed he had discussed Biden with Zelensky and confirmed he slow-walked aid to Ukraine, although he claimed the two acts were unrelated. That call and a whistleblower complaint involving Mr. Trump have pushed growing numbers of Democrats to call for impeachment proceedings, which are now formally beginning, House Speaker Nancy Pelosi announced Tuesday afternoon.

Responding to the release of the memorandum, Mr. Trump told reporters Wednesday that he was subject to "the single greatest witch hunt in American history, probably in history." Mr. Trump said "there was no pressure whatsoever" put on Zelensky, adding that "it turned out to be a nothing call." He slammed "fake news" and "corrupt reporting" about the phone call.

When asked by reporters about the call on Wednesday in a joint press conference with Mr. Trump, Zelensky said that "nobody pushed me."

In a statement, Justice Department spokesperson Kerri Kupec said that the Justice Department had determined that "there was no campaign finance violation and that no further action was warranted."

"In August, the Department of Justice was referred a matter relating to a letter the director national intelligence had received from the inspector general for the intelligence community regarding a purported whistleblower complaint. The inspector general's letter cited a conversation between the president and Ukrainian President Zelensky 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.

"Relying on established procedures set forth in the justice manual, the department's criminal division reviewed the official record of the call and determined based on the facts and applicable law that there was no campaign finance violence and that no further action was warranted. All relevant components of the department agreed with this legal conclusion, and the department has concluded this matter," Kupec concluded.

In another statement, Kupec said that Barr had not spoken with Mr. Trump about Ukraine investigating Biden, and that the president had not asked Barr to contact Ukraine or Giuliani.

The Justice Department's Office of Legal Counsel (OLC) determined that the complaint needed to have a "connection with the operation of any U.S. Government intelligence activity, and the alleged misconduct does not involve any member of the intelligence community" in order to qualify as an "urgent concern." The OLC found that since the president is not a member of the intelligence community and that the activity in question did not pertain to any ongoing intelligence matters, that the complaint did not meet the standard of an "urgent concern."

Mr. Trump had previously said he hoped the public would see the transcript, but he feared the precedent it might set for other world leaders who want to keep their conversations with him private.

Biden, who called for the release of the transcript, said the summary showed that Mr. Trump "implored the President of Ukraine to work with his personal attorney to manufacture a smear against a domestic political opponent" and planned to involve the United States Department of Justice."

The phone call is just one part of a whistleblower complaint Democrats want to see. Biden and Democrats are calling for the full whistleblower complaint that has yet to be turned over to the House Intelligence Committee. Chairman Adam Schiff tweeted Tuesday that the whistleblower wants to testify before his committee.