The Internal Revenue Service on Friday apologized for targeting groups with “tea party” or “patriot” in their names, confirming long-standing accusations by some conservatives that their applications for tax-exempt status were being improperly delayed and scrutinized.

Lois G. Lerner, the IRS official who oversees tax-exempt groups, said the “absolutely inappropriate” actions by “front-line people” were not driven by partisan motives.

Rather, Lerner said, they were a misguided effort to come up with an efficient means of dealing with a flood of applications from organizations seeking ­tax-exempt status between 2010 and 2012.

During that period, about 75 groups were selected for extra inquiry — including burdensome questionnaires and, in some cases, improper requests for the names of their donors — simply because of the words in their names, she said in a conference call with reporters.

They constituted about one-quarter of the 300 groups who were flagged for additional analysis by employees of the IRS tax-exempt unit’s main office in Cincinnati.

It was not clear whether the IRS had anticipated the firestorm that it would ignite with its disclosure. Indeed, it appeared to have happened by chance when Lerner, appearing Friday at a conference held by the American Bar Association, responded to a question about the allegations by conservative groups.

The IRS’s subsequent conference call with reporters was clumsily handled. At one point, Lerner attempted to do arithmetic on the phone and blurted out: “I’m not good at math.” That admission was understandable, given that her training is as a lawyer, but it produced a quote that is likely to haunt the agency that handles the nation’s tax returns.

Nor did IRS officials appear to have prepared much for the questions they would get.

“The IRS did not acknowledge the use of names as part of the process earlier because the details were not initially known to senior leadership, and [the Treasury inspector general for tax administration] has been reviewing the situation,” IRS spokeswoman Michelle L. Eldridge said. “Their work is now far enough along that it was appropriate to address the issue when it came up during today’s tax conference.”

Of the 300 groups affected, the IRS said, 130 have had their tax-exempt status approved and 25 have withdrawn their applications.

The sensitivity arises in no small part because of the IRS’s history as an agency that presidents have used to intimidate, harass and punish their political enemies. Most infamous was Richard M. Nixon, but the practice went back at least as far as Franklin D. Roosevelt. ­Post-Watergate reforms made the IRS more independent and were designed to insulate it from politics.

“I call on the White House to conduct a transparent, government-wide review aimed at assuring the American people that these thuggish practices are not underway at the IRS or elsewhere in the administration against anyone, regardless of their political views,” Senate Minority Leader Mitch McConnell (R-Ky.) said. “An apology won’t put this issue to rest.”

One of the nation’s largest tea party groups, the Tea Party Patriots, said it rejected the IRS’s explanation and demanded the resignations of all officials involved. The group also called on President Obama to apologize for ignoring its concerns.

“The IRS has demonstrated the most disturbing, illegal and outrageous abuse of government power,” said Jenny Beth Martin, national coordinator of Tea Party Patriots. “This deliberate targeting and harassment of tea party groups reaches a new low in illegal government activity and overreach.”

Lerner said she has had no contact with Obama administration officials about the issue.

When questioned by reporters, she said the problem came to the IRS’s attention only after officials read reports in the media of complaints by tea party groups that their applications for ­tax-exempt status were being unfairly scrutinized and delayed.

Although the IRS is part of the Treasury Department, it “is an independent enforcement agency,” White House press secretary Jay Carney said. “What we know about this is of concern and we certainly find the actions taken, as reported, to be inappropriate. And we would fully expect the investigation to be thorough and for corrections to be made in a case like this.”

Carney did not describe what contact, if any, administration officials have had with the IRS regarding the issue.

The IRS admission comes amid a debate about when political groups on both sides deserve tax-exempt status — a complex question that turns on whether the group is working mainly to support a general philosophy or a specific party or candidate.

That can be particularly difficult to determine in the case of groups that operate under section 501(c)(4) of the Internal Revenue Code. The law grants them an exemption from income taxes on the contributions they receive if they are “social welfare” groups.

It also allows them to engage in political activity and advocacy as long as it is not their primary mission. And while donors to those organizations are not allowed a tax deduction for what they give, they can remain anonymous.

The number of organizations applying for tax-exempt status under that provision more than doubled after 2010, Lerner said. It was a scramble that began after the Supreme Court lifted the ban on corporate and union spending in political campaigns, a move that was seen as a green light for outside groups to become more involved, as well.

Both Democratic- and Republican-allied interests have formed such organizations, but the conservative groups have raised vastly more money.

The IRS disclosure comes after more than a year of tense debate about the tax status of conservative political groups. Tea party groups and other conservative organizations have said that they have been the subject of inappropriate screening by the IRS, prompting formal complaints by Republican lawmakers. The IRS inspector general has been reviewing the claims.

Some Democrats and campaign finance groups, meanwhile, have argued that ­tax-exempt groups are stretching the boundaries of the law and should be required to disclose more about their operations.

Sen. Orrin G. Hatch (Utah), the top Republican on the Senate Finance Committee, who has raised concerns about IRS oversight of conservative groups, said he was not satisfied by the apology.

“This, frankly, isn’t enough,” he said. “We need to have ironclad guarantees from the IRS that it will adopt significant protocols to ensure this kind of harassment of groups that have a constitutional right to express their own views never happens again.”

Lerner would not say whether any of the IRS employees involved have been disciplined. She said that policies have been put in place to prohibit this kind of screening and that so far, none of the 75 groups has been rejected for tax-exempt status.

Jay Sekulow, a lawyer representing 16 tea party groups, said Friday that he was gratified by the IRS acknowledgment.

“This admission by the IRS represents a significant victory for free speech and freedom of association,” he said. “There was never any doubt that these organizations complied with the law and applied for tax-exempt status for their activities as Americans have done for decades.”