WASHINGTON — F.B.I. officials had sufficient reason to open the investigation into links between Russia and Trump campaign aides in 2016 and acted without political bias, a long-awaited report said on Monday, but it concluded that the inquiry was a rushed and dysfunctional process marked by serious errors in documents related to a wiretap.

The exhaustive report by the Justice Department’s independent inspector general, Michael E. Horowitz, faced an immediate challenge. Attorney General William P. Barr sought to undermine the key finding that investigators had an adequate basis to open the inquiry, known as Crossfire Hurricane.

“The inspector general’s report now makes clear that the F.B.I. launched an intrusive investigation of a U.S. presidential campaign on the thinnest of suspicions that, in my view, were insufficient to justify the steps taken,” Mr. Barr, a close ally of President Trump who has begun his own re-investigation of the Russia inquiry, said in a statement.

Yet Mr. Horowitz stressed that the standard for opening an F.B.I. investigation was low — echoing the sort of criticism that civil libertarians have made for years. He also exonerated former F.B.I. leaders, broadly rejecting Mr. Trump’s accusations that they engaged in a politicized conspiracy to sabotage him.

“We did not find documentary or testimonial evidence that political bias or improper motivation influenced” officials’ decision to open the investigation, the report said.

At the same time, Mr. Horowitz’s report was scathing about other aspects of the sprawling inquiry, documenting serious and systematic problems with the F.B.I.’s handling of applications to win court orders to wiretap Carter Page, a former Trump campaign adviser. Mr. Horowitz said investigators appeared to overstate the strength of their applications, and he separately referred one low-ranking F.B.I. lawyer for possible prosecution for altering a related document.

By puncturing conspiracy theories promoted by Mr. Trump and his allies, yet sharply criticizing law enforcement actions that have not been the subject of public debate, Mr. Horowitz’s mixed findings offered a basis for both critics and allies of Mr. Trump to claim vindication. The report by an independent official presented a definitive accounting of the F.B.I.’s actions in the early stages of the Russia investigation.

Mr. Horowitz recommended re-evaluating and tightening procedures and said his office had begun a broader audit of surveillance applications targeting Americans. In an 11-page response, the F.B.I. director, Christopher A. Wray, said he was ordering 40 corrective steps to address the report’s recommendations.

The Horowitz report, as well as Mr. Barr’s criticism, is certain to extend the debate over the legitimacy of the F.B.I.’s inquiry, which grew into the special counsel investigation led by Robert S. Mueller III.

The report also rebuffed other conservative claims that the F.B.I. spied on the Trump campaign as part of a politicized plot. It confirmed that the F.B.I. opened the inquiry in July 2016 as stolen Democratic emails spilled out and investigators learned that a Trump campaign aide bragged that he had been told that Russia had information that could damage Hillary Clinton. Investigators did not open the inquiry based on a notorious dossier of opposition research from Christopher Steele, a former British spy whose research was funded by Democrats, Mr. Horowitz found.

Nor did the F.B.I. send informants or undercover agents to meet with campaign officials before opening Crossfire Hurricane, place any informants inside the campaign or ask the informants it did rely on to “report on the Trump campaign,” as Mr. Trump’s allies have insinuated.

In comments after Mr. Horowitz’s report was made public, Mr. Trump nevertheless reprised his attacks on the Russia investigation as an attempted coup and a conspiracy. He claimed — in opposition to the report’s findings — that it showed “an attempted overthrow, and a lot of people were in on it and they got caught, they got caught red-handed.”

Mr. Barr praised Mr. Horowitz’s work but excoriated the F.B.I. investigation, saying the bureau’s “malfeasance and misfeasance” detailed in the report reflected a “clear abuse” of the wiretap application process. Mr. Barr has publicly said he thinks the F.B.I. subjected the Trump campaign to “spying” and tapped John H. Durham, the United States attorney in Connecticut, to lead yet another investigation into the Russia inquiry.

Shortly after the report was made public on Monday, the Justice Department issued an extraordinary statement in Mr. Durham’s name objecting to the inspector general’s findings as well. Based on the evidence he has gathered, Mr. Durham said, he had recently “advised the inspector general that we do not agree with some of the report’s conclusions as to predication and how the F.B.I. case was opened.”

Mr. Durham, a veteran of high-profile political investigations who is known for keeping quiet during his inquiries, did not specify any additional evidence he had uncovered that might credibly undermine Mr. Horowitz’s assessment that F.B.I. officials met the standard in 2016 for opening an investigation.

“I look forward to the Durham report, which is coming out in the not-too-distant future,” Mr. Trump said. “It’s got its own information, which is this information plus plus plus.”

James B. Comey, the F.B.I. director who oversaw the opening of the Russia investigation and whom Mr. Trump abruptly fired nearly a year later, lauded Mr. Horowitz’s findings and called on “those who attacked the F.B.I.” to acknowledge they were wrong.

“The allegation of a criminal conspiracy was nonsense,” Mr. Comey, citing Mr. Horowitz’s findings, wrote in an op-ed article in The Washington Post. “There was no illegal wiretapping, there were no informants inserted into the campaign, there was no ‘spying’ on the Trump campaign.”

While Mr. Horowitz concluded that investigators followed existing rules in opening Crossfire Hurricane, he portrayed those rules as lax in permitting the bureau to take many key steps without higher-level approval from Justice Department officials.

For a full investigation, which permits wiretapping, F.B.I. procedures require an “articulable factual basis” that “reasonably indicates” that a crime or a national security threat exists. The bureau’s top counterintelligence agent, Bill Priestap, decided after deliberating with senior colleagues that the standard had been met, Mr. Horowitz found.

Much of the report focused on the documents associated with the wiretapping of Mr. Page. Despite the attention it has received, the wiretap was but a small piece of a sprawling F.B.I. investigation into Russian election interference. Investigators obtained nearly 500 search warrants and interviewed hundreds of witnesses, according to the special counsel’s report.

The FISA court first approved the wiretap in October 2016, about a month after Mr. Page had stepped down from the Trump campaign. The Justice Department obtained three renewals of court permission to eavesdrop on Mr. Page — two under the Trump administration.

Given the highly fraught context of investigating someone linked to a presidential campaign, the report said, the Crossfire Hurricane investigators knew their work would be scrutinized — yet they nevertheless “failed to meet the basic obligation to ensure that the Carter Page FISA applications were ‘scrupulously accurate.’”

The findings on the wiretap application showed that when it mattered most — with the stakes the greatest and no room for error — F.B.I. officials still made numerous and serious mistakes in wielding a powerful surveillance tool. Mr. Horowitz’s discovery calls into question the bureau’s surveillance practices in routine cases.

A chart in the report listed dozens of significant inaccuracies, omissions or assertions that investigators failed to back up in supporting documents in the four applications. To make the case that Mr. Page was probably a foreign agent, they relied on historical information about his contacts with Russians before 2016 and claims about his 2016 interactions with Russians that came from the Steele dossier.

Among the problems: The F.B.I. never told the Justice Department, which thus never told the court that granted permission for the wiretaps, that Mr. Page had for years been providing information to the C.I.A. about his prior contacts with Russian officials — including an encounter cited in the application as a reason to be suspicious of him. That might have made his history less suspicious.

The F.B.I.’s omission of Mr. Page’s contacts with the C.I.A. relates to the criminal referral that Mr. Horowitz made about an F.B.I. lawyer assigned to assist the Russia investigation team. He found that the lawyer, whom people familiar with the inquiry have identified as Kevin Clinesmith, altered an email from the C.I.A. to a colleague during a renewal application. (The report identified neither Mr. Clinesmith nor the C.I.A. by name.)

An F.B.I. official who had to sign an affidavit attesting to the accuracy and completeness of a court filing had specifically asked about any relationship with the C.I.A. Mr. Clinesmith altered the email so that it stated that Mr. Page was “not a source,” contributing to the Justice Department’s failure to discuss his relationship with the C.I.A. in a renewal application.

Many of the problems Mr. Horowitz identified centered on the use of the Steele dossier, which his report portrayed as “essential” to establishing for the FISA court that investigators had probable cause to suspect that Mr. Page was an agent of a foreign power. The initial application relied on four claims from the dossier, and the credibility of each eroded over time.

Among other flaws uncovered by the inspector general, the F.B.I. in January 2017 interviewed a primary source of Mr. Steele’s for important claims about Mr. Page. The source contradicted some of what Mr. Steele had written. But F.B.I. officials said only that they found the source “truthful and cooperative,” leaving the false impression in renewal applications that his account had confirmed — rather than raised doubts about — the dossier’s reporting.

“The three Carter Page renewal applications contained a number of factual representations that were inaccurate, incomplete or unsupported by appropriate documentation, based upon information in the F.B.I.’s possession at the time the applications were filed,” the report said.

It placed primary blame for the significant errors and omissions on sloppiness by F.B.I. case agents. But it also portrayed the problems as a leadership failure by senior officials, and recommended that the F.B.I. review the performance of every employee involved in the effort.

The inspector general found that this pattern was not intentional, but that explanations — such as that the agents were busy with the Russia investigation at the time and that “the Carter Page FISA was a narrow aspect of their overall responsibilities” — were unsatisfactory.

Mr. Horowitz took no position on whether a judge would have approved the wiretap without the misstatements and omissions.

In addition, the inspector general looked at the role of a Justice Department official named Bruce G. Ohr, who has been vilified by Mr. Trump and his allies because he was in contact with Mr. Steele and because his wife worked for the political research firm that employed Mr. Steele.

The inspector general did not accuse Mr. Ohr of being part of a conspiracy. But he criticized Mr. Ohr for “consequential errors in judgment,” including failing to keep his supervisors informed of his actions and making himself “a witness” in the investigation. He also suggested that the department’s Office of Professional Responsibility review Mr. Ohr’s conduct.