Justice Department officials took less than a month to abandon an inquiry into President Trump’s communications with his Ukrainian counterpart about investigating former vice president Joe Biden — reigniting concerns among Democrats and legal observers that the law enforcement agency is serving as a shield for the commander in chief.

Just weeks after intelligence leaders asked the Justice Department and FBI to consider examining a summer phone call between Trump and Ukrainian President Volodymyr Zelensky, the head of the department’s criminal division determined there was not sufficient cause to even launch an investigation, senior Justice Department officials said.

Department officials and career public integrity prosecutors reviewed a rough transcript of the call and verified its authenticity, but — because a case was not opened — took no other steps, such as conducting interviews, the officials said. They looked only at whether Trump might have violated campaign finance laws, not federal corruption statutes, even though some legal analysts said there seemed to be evidence of both.

Repeatedly in the July 25 phone call, Trump pressed Zelensky to launch an investigation into Biden and his son, and to greenlight another inquiry into the origins of the special counsel probe that once dogged Trump’s presidency, according to a rough transcript released by the administration Wednesday. He interspersed his demands with casual references to help that the U.S. government had given Ukraine, and a vague promise of how Zelensky might one day be able to meet Trump at the White House, the document shows.

Legal analysts said that was suggestive not only that Trump was seeking a contribution from a foreigner — which would violate campaign finance laws — but that he also seemed to hint at a corrupt bargain in which Zelensky would get a White House meeting or other help in exchange for digging up dirt on Trump’s political foe.

“I was really startled that they put this out there with the spin that they thought it was somehow exculpatory,” said Randall Eliason, a former federal prosecutor in Washington. “When I look at it, I’m like, ‘Holy cow.’ ”

Senior Justice Department officials defended their handling of the matter, saying that campaign finance laws required them to “quantify” the value of what Trump was seeking for his campaign, and that was impossible to do with the investigations Trump had requested. They said they were examining what was referred, and the rough transcript of the call was the “best evidence” to help determine what to do.

The officials spoke on the condition of anonymity to discuss internal deliberations. Kerri Kupec, a Justice Department spokeswoman, said in a statement that the head of the Justice Department’s criminal division determined that “there was no campaign finance violation and that no further action was warranted.”

“All relevant components of the Department agreed with his legal conclusion, and the Department has concluded the matter,” Kupec said. She said that although Trump mentioned Barr in the call, the president had “not spoken with the Attorney General about having Ukraine investigate anything related to former Vice President Biden or his son,” nor had Barr discussed Ukraine with Giuliani.

The department’s Office of Legal Counsel has opined that a sitting president cannot be indicted — although officials said that was not a part of the calculus in this instance. A president can be charged after leaving office.

Even before the Justice Department’s decision was made public, House Speaker Nancy Pelosi (D-Calif.) said Democrats would conduct an impeachment inquiry into Trump — which need not find technical violations of campaign finance or bribery laws.

“It is still within Congress’s power to impeach and remove by viewing this as an abuse of power,” said Richard L. Hasen, a University of California at Irvine law professor specializing in election law. “Whether it’s a crime is secondary to the impeachment inquiry. It could be relevant if Trump is out of office and somebody wants to try to prosecute him.

The matter first came to the Justice Department’s attention in late August, soon after the inspector general for the intelligence community gave to the acting director of national intelligence a whistleblower complaint alleging that unnamed White House officials had expressed concern about Trump’s call.

The inspector general determined that the complaint represented an “urgent” concern, and should be forwarded to the congressional intelligence committees. But the acting director of national intelligence contacted the Justice Department, wondering whether the unusual circumstances warranted something else.

The Justice Department’s Office of Legal Counsel and its head, Steven A. Engel, soon began exploring what to do. According to senior Justice Department officials, the acting director of national intelligence around the same time made a criminal referral, passing to the department the inspector general’s concern that campaign finance laws might have been violated.

On Sept. 3, Engel issued a classified memo declaring that the acting director of national intelligence need not turn over the complaint to Congress. Such a step would be taken only if the complaint was about an intelligence activity, Engel wrote in a later, public version of the document. The whistleblower’s secondhand allegation about Trump’s call, he wrote, would be more properly referred to the Justice Department.

Rep. Adam B. Schiff (D-Calif.), the chair of the House Intelligence Committee, said that decision “throws the leadership of that department into further ill repute.”

On Sept. 4, the inspector general made a separate, written referral to the FBI, senior Justice Department officials said. By that time, the officials said, the Justice Department already had assigned its criminal division and public integrity prosecutors — which normally handle campaign finance cases — to explore whether there was enough evidence to open an investigation. The FBI, the officials said, deferred to the Justice Department. An FBI spokeswoman declined to comment.

On Sept. 9, the inspector general notified Congress of the complaint, but did not share its contents. A day later, Schiff demanded to see it. On Sept. 18, The Washington Post reported that it involved Trump’s communications with a foreign leader and some kind of “promise.”

That very week — unbeknown to the public — the Justice Department decided there was not enough evidence to proceed with a campaign finance investigation. The decision, senior Justice Department officials said, was made by Brian Benczkowski, who heads the Justice Department’s criminal division. They said career prosecutors agreed with the decision.

The officials said Barr was “generally knowledgeable” of discussions about the Office of Legal Counsel decision, but was not involved in making the call not to move forward with an investigation. Legal analysts and Democrats said Wednesday that Barr should step aside from the matter entirely.

“The President dragged the Attorney General into this mess,” Rep. Jerrold Nadler (D-N.Y.), the chair of the House Judiciary Committee, wrote on Twitter. “At a minimum, AG Barr must recuse himself until we get to the bottom of this matter.”

Barr has previously faced criticism from Democrats for shielding Trump, especially in his descriptions of special counsel Robert S. Mueller III’s report on whether the president had conspired with the Russians to influence the 2016 election. Before the report was released, Barr offered what he termed its “principal conclusions” and hewed closely to Trump’s favorite talking points on the special counsel investigation: no collusion, no obstruction. Mueller complained later that Barr’s characterization “did not fully capture the context, nature, and substance” of his work.

The criminal divisions’s analysis of Trump’s call essentially started and ended with the decision that a Ukrainian investigation into Biden could not be assigned a specific value.

“If you cannot quantify what the thing of value would be, then it’s fatal,” a senior Justice Department official said.

Mueller had to wrestle with a similar question as he examined the Trump campaign’s July 2016 meeting at Trump Tower with a Russian lawyer who had offered derogatory information on Hillary Clinton, Trump’s opponent in the presidential race. Mueller’s team wrote in its report that “candidate-related opposition research” could be a contribution and potentially break the law, if it came from a foreign source. But they also noted that “no judicial decision has treated the voluntary provision of uncompensated opposition research or similar information as a thing of value that could amount to a contribution under campaign-finance law.”

Hasen, the law professor, said he thought the Justice Department’s determination that Trump’s request could not be quantified was “laughable.”

“You’re talking about information on a potential rival that could be used in a presidential campaign, a presidential campaign which likely would run into the billions of dollars,” Hasen said. “I don’t think there’s any question that a prosecutor could go forward with the theory.”

For his part, Trump seemed to focus on another allegation that legal analysts said he might have faced: trying to extort or solicit a bribe from Ukraine’s government. The president insisted he had not offered a “quid pro quo” to his Ukrainian counterpart, which is an aspect of a federal corruption case.

“It’s all a hoax, folks, it’s all a big hoax,” he said in New York on Wednesday. “No push, no pressure, no nothing . . . There was no quid pro quo.”

Legal analysts noted that the context of Trump’s call — at the time, the administration was withholding hundreds of millions of dollars in aid from Ukraine at Trump’s direction — suggests he was trying to strike a bargain. Eliason, the former federal prosecutor, noted that in most bribery cases, those accused seldom offer an explicit bargain.

“You normally don’t have a quid pro quo stated expressly,” Eliason said. “This is almost as close as you can get.”