The Justice Department’s Criminal Division has already investigated President Trump’s conversation with the Ukrainian president about Joseph R. Biden and concluded Mr. Trump did not violate campaign finance laws, officials announced Wednesday.

And a separate division of the department has also ruled that the administration did not break the law by failing to quickly share a whistleblower’s complaint with Congress, saying the matter didn’t meet the definition of “urgent” that would trigger the law.

The department also released the transcript of Mr. Trump’s conversation with Ukrainian President Volodymyr Zelensky, showing the American leader did talk about Mr. Biden, the former vice president and current Democratic presidential front-runner, and his son, Hunter Biden. But Mr. Trump did not threaten to withhold military aid as some have alleged.

Mr. Trump did tell President Volodymyr Zelensky that his personal attorney Rudolph W. Giuliani and Attorney General William P. Barr would reach out to him to discuss the Biden case.

“I will have Mr. Giuliani give you a call and I am also going to have Attorney General William Barr give you a call and we will get to the bottom of it,” Mr. Trump said, according to the transcript of the call reviewed by The Washington Times.

And Mr. Trump said it would be “great” if Ukraine reopened its investigation.

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“The other thing, there’s a lot of talk about Biden’s son, that [Joe] 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,” Mr. Trump said according to the transcript. “Biden went around bragging that he stopped the prosecution. See if you can look into it….it sounds horrible to me.”

Mr. Zelensky appeared receptive to reviewing the Hunter Biden probe, saying a newly appointed prosecutor will “look into the situation.”

“The issue of the investigation of the case … so we will take care of that and work on the investigation of the case,” he said.

Justice Department spokeswoman Kerri Kupec said the attorney general was first made aware of the call several weeks after the July conversation between the two world leaders.

“The president has not spoken with the attorney general about having Ukraine investigate anything related to former Vice President Biden or his son,” she said in a statement. “The President has not asked the attorney general to contact the Ukraine — on this or any other matter.”

“The attorney general has not communicated with Ukraine — on this or any other subject. Nor has the attorney general discussed this matter, or anything relating to Ukraine with Rudy Giuliani,” she continued.

Also, during the conversation, Mr. Trump appears to imply a missing server from the Democrat National Committee is located in Ukraine.

“I would like you to do us a favor though our country has been through a lot and Ukraine knows about it,” he said. “I would like you to find out what happened with this whole situation with Ukraine. They say crowd strike…The server, they say Ukraine has it.”

That conversation has turned into a firestorm in Washington, where House Speaker Nancy Pelosi says it amounts to a breach of the president’s oath of office and is troubling enough to launch an impeachment inquiry.

Mr. Trump has insisted the conversation was innocent.

A whistleblower reported the conversation to authorities Aug. 12, citing information from “White House officials” and saying it appeared Mr. Trump was trying to pressure Ukraine to assist in his 2020 election.

The intelligence community inspector general concluded that the whistleblower showed political bias — but said the report was still credible and urgent enough that it needed to be shared with Congress by the Director of National Intelligence.

But the Justice Department’s Office of Legal Counsel said that’s not the case.

“The question is whether such a complaint falls within the statutory definition of ‘urgent concern’ that the law requires the DNI to forward to the intelligence committees. We conclude that it does not,” wrote Steven A. Engel, assistant attorney general at the OLC.

They also ruled that the president’s conversation was a diplomatic communication and not an intelligence activity, and the president isn’t a part of the intelligence community anyway, so his behavior is not part of the DNI’s purview.

“Such matters simply do not relate to ‘the funding, administration or operation of an intelligence activity within the responsibility and authority’ of the DNI,” Mr. Engel concluded.

He said if anything, the Justice Department should be the ones to investigate.

And indeed that happened. The Justice Department’s criminal division said it probed the conversation as a possible violation of campaign finance laws, wondering if Mr. Trump had solicited a contribution of sorts by asking Ukraine to probe an opponent.

The department said it concluded that wasn’t the case.

The review came in late August when intelligence officials referred the matter to the Justice Department’s criminal division to see if the president’s comments violated laws barring candidates requesting assistance from foreign sources.

Intelligence officials also made a separate referral to the FBI, which was rerouted back to the Justice Department.

After reviewing a transcript of the call, prosecutors concluded there was no appropriate reason for a criminal investigation. But senior officials acknowledged the department’s review did include interviews with potential witnesses to the phone call or others who may have had relevant information.

Those same officials also the review was closed because help from a foreign country could not be considered “a thing of value” under campaign finance law. Federal law defines a “thing of value” has any assistance provided to a campaign and it is not limited to monetary donations.

Ms. Kupec said the Justice Department relied on “established procedures” and determined “there was no campaign finance violation and no further action was warranted.

“All relevant components of the department agreed with this legal conclusion and the department has concluded the matter,” she said.

Justice officials said Mr. Barr was aware of the inspector general’s referral, but he did not make the final decision to reject initiating a criminal investigation of the president.