Federal authorities have opened a criminal investigation of whether Internal Revenue Service employees broke the law when they targeted conservative groups seeking tax-exempt status — the latest setback for an agency that is the subject of withering bipartisan criticism and multiple congressional inquiries.

Attorney General Eric H. Holder Jr. said Tuesday that the Justice Department and the FBI began the probe after the IRS acknowledged that it selected conservative groups with the words “tea party” and “patriot” in their names for special reviews.

“We are examining the facts to see if there were criminal violations,” Holder said at a news conference.

Also Tuesday, a widely anticipated report by the IRS’s watchdog described the agency’s tax-exempt unit — where the screening of conservative groups occurred — as a bureaucratic mess, with some employees ignorant about tax laws, defiant of their supervisors and blind to the appearance of impropriety.

The report by the Treasury Inspector General for Tax Administration described in detail the use of “inappropriate criteria” to screen political advocacy groups. An IRS unit created a “lookout” list for organizations with keywords such as “tea party” or “patriot” in their names. Organizations faced months of delays in getting their applications approved.

President Obama in a statement on Tuesday called the report’s findings “intolerable and inexcusable,” adding that he has directed Treasury Secretary Jack Lew “to hold those responsible for these failures accountable, and to make sure that each of the Inspector General’s recommendations are implemented quickly, so that such conduct never happens again.”

IRS officials told the inspector general that they had used the keywords as shorthand to efficiently manage a deluge of new political advocacy groups, but that explanation was rejected by the inspector general’s office.

“Developing and using criteria that focuses on organization names and policy positions instead of the activities . . . does not promote public confidence that tax-exempt laws are being adhered to impartially,” said the report, which Inspector General J. Russell George issued.

The report did not find evidence that the actions were motivated by partisan interests. IRS officials told investigators they did not consult anyone outside the agency about the screening.

The watchdog report is likely to stoke growing outrage over the agency’s actions. No IRS employees involved in the decisions have been disciplined, and one has been promoted, said House Oversight and Government Reform Committee Chairman Darrell Issa (R-Calif.), whose panel prompted the audit.

“We still do not know why the targeting began, how extensive it was, who initiated it and who knew about it,” said Rep. Jim Jordan (R-Ohio), a member of the oversight committee. “The IRS must be held accountable to the American people, which requires a full investigation.”

In a written response attached to the watchdog report, Joseph Grant, acting commissioner of tax-exempt and government entities at the IRS, conceded that “some errors occurred” but pledged that “significant improvements in this area are in place and we are confident that what transpired here will not recur.”

The IRS firestorm began Friday after Lois G. Lerner, the IRS official who oversees tax-exempt groups, acknowledged and apologized at a legal conference for the targeting. The Justice Department and the FBI began investigating later that day, a Justice Department official said.

“The investigation is in its early stages, and the department is looking at various laws governing the misconduct of government employees” in the federal criminal code or the federal tax code, the official said.

David H. Laufman, a former Justice Department lawyer, said that although there may be a range of administrative actions that could be taken against IRS employees for their conduct, it may be difficult to prosecute them criminally unless they intentionally violated the law.

“Willfulness would not exist where [IRS employees] believed they were acting in good faith or they were negligent in some respect,” Laufman said. “For there to be a criminal violation, there will have to be evidence beyond a reasonable doubt that someone at the IRS knowingly and willfully violated the law.”

Conservatives pressed for additional action. Daniel Epstein, executive director of Cause of Action, a D.C.-based conservative group, wrote to federal prosecutors urging them to convene a grand jury, saying IRS employees may have “engaged in a conspiracy” to block members of conservative groups from exercising their constitutional rights.

Four committees in both chambers of Congress also are looking into the actions, with the House Ways and Means Committee to hold the first hearing on Friday.

The IRS watchdog’s report painted a dark picture of the tax-exempt unit at the IRS. It said the decision to focus on groups with conservative-sounding names originated in the IRS “determinations unit” in Cincinnati in early 2010. Officials blacked out any details of what prompted the decision.

In May 2010, the office “began developing a spreadsheet that would become known as the ‘Be On the Look Out’ listing,” according to the report, including applications from tea party groups. “By July 2010, Determinations Unit management stated that it had requested its specialists to be on the lookout for Tea Party applications.”

The report said the IRS officials had a range of criteria for potential political cases that included the terms “tea party,” “patriots” and “9/12 Project”; issues such as government spending, government debt or taxes; education of the public about how to “make America a better place to live”; and a statement in the case file criticizing how the country is being run.

The report states that these labels were applied by front-line employees who “showed a lack of knowledge in the Determinations Unit of what activities are allowed” for tax-exempt organizations. They demanded information, including donor lists, that were wrong to request during the application process for nonprofit status, investigators said.

Lerner objected to the Cincinnati unit’s criteria for identifying which groups should receive stricter scrutiny in late June 2011. A week later, the unit adopted a broader definition, focused on the “political, lobbying, or [general] advocacy” activities of applications.

But, the report notes, “The team of specialists subsequently changed the criteria in January 2012 without executive approval because they believed the July 2011 criteria were too broad.”

The officials subjected 296 political advocacy groups to heightened scrutiny, including 72 “tea party” groups, 13 “patriot” groups and 11 “9/12” groups, named for a movement associated with conservative commentator Glenn Beck. As of last year, 108 of those applications had been approved, 28 had been withdrawn and none had been denied, the report said. Some of the remaining 160 open cases have been outstanding for up to three years, encompassing two elections.

Officials from the IRS and the inspector general’s office have also told congressional aides that senior officials, including acting IRS Commissioner Steven T. Miller and former commissioner Douglas Shulman, were briefed on the actions after the targeting occurred.

Republican lawmakers say Miller and Shulman did not inform Congress about what they learned, despite numerous inquiries. Shulman was a George W. Bush appointee; Miller is a career IRS employee.

Although the IRS has taken actions to fix the problems, acting Deputy Inspector General Michael E. McKenney made clear in a memo Tuesday that investigators believe the agency has not fixed its problems.

Until lingering cases are settled, he wrote, “we do not consider the concerns in this report to be resolved.”

Ed O’Keefe contributed to this report.