President Obama’s plan to keep FBI Director Robert S. Mueller III in office beyond his 10-year term has triggered an angry reaction among some agents, who say Muel­ler imposed term limits on hundreds of supervisors in the agency but is failing to abide by legal limits set on his own tenure.

The accusations of hypocrisy come as Congress is considering whether to grant Obama’s request to allow Mueller two more years in office — an extension the president said would provide stability as other national security agencies undergo major transitions in leadership.

“We understand the desire for stability,’’ said Konrad Motyka, president of the FBI Agents Association, which is renewing its call for an end to the term-limit policy. “But people are saying, ‘What about my stability?’ It’s ironic that this desire for stability did not apply to supervisors within the FBI.’’

The FBI’s policy, which is unusual among law enforcement agencies, was adopted after the Sept. 11, 2001, terrorist attacks. Known as “up or out,’’ it requires FBI supervisors to leave their posts after seven years and compete for other managerial jobs, retire or accept a demotion in the same field office with lower pay.

FBI officials say the term limits have brought strong managers into hundreds of positions created in the years after Sept. 11. But the plan to retain Mueller has revived long-simmering tensions over the policy, which some say has robbed the bureau of veteran supervisors who retired because they did not get promoted.

Some agents, speaking on the condition of anonymity for fear of retaliation, expressed anger at the thought of Mueller staying when others have left.

“People are up in arms about this,’’ said one agent, who likened the news to “a shot in the kneecaps.’’

“We have lost valuable experience,’’ the agent said. “I’ve seen people, some really significant contributors to this organization and to this country, who are questioning their self-worth now and who are basically bitter.’’

White House officials declined to comment beyond Obama’s statement last week. A spokesman for Mueller declined to comment, citing the pending request to extend Mueller’s tenure. No significant opposition to the proposal has emerged in Congress, where Mueller generally enjoys bipartisan support.

The request has drawn strong support from congressional Democrats, Attorney General Eric H. Holder Jr. and the FBI Intel­ligence Analysts Association, which on Wednesday called Mueller “a tremendous catalyst and leader.’’

Justice Department officials and former FBI officials say Mueller, who took over the post a week before the 2001 attacks, has a strong record and has successfully led the effort to prevent another terrorist strike in the United States. They say the dispute reflects resistance to change at the tradition-bound agency, which has added nearly 3,000 agents since the attacks, has tripled the number of analysts and is transforming into an intelligence agency focused on preventing terrorist strikes.

“Any organization which underwent such dramatic change will always produce a small group of detractors,’’ said Neil H. MacBride, the U.S. attorney in Alexandria, who has worked extensively with Mueller and said his initiatives have been “transformative.’’

Michael Heimbach, who was Mueller’s assistant director of counterterrorism until 2009, said Mueller’s term limit is “totally different than up-or-out. . . . He’s leading the FBI. He’s not supervising a squad.’’

An FBI official, speaking on the condition of anonymity because of the sensitivity of the issue, said Mueller did not seek the extension and considered it carefully.

“This is a term limit. There’s a statute,’’ the official said. “But when the president calls and you’re the type of guy the director is, it’s very hard to say no.’’

The official said that “you’d have to be blind not to see that there is irony” in Mueller’s decision to stay, but added: “We’re at the highest [terrorist] threat level we’ve ever been. This isn’t the time to change directors.’’

Heimbach said Mueller, a former Marine, may have alienated some agents in the FBI’s “old guard” with his hard-driving, demanding style. Some agents also criticized Mueller in interviews this week as too top-down, aloof and not focused on their concerns.

“Did I like getting up at 4:30 every morning and facing him at 7? Heck no,’’ Heimbach said. “But I respected him, and I can’t imagine the president not wanting to keep him.’’

The up-or-out policy emerged after hundreds of FBI jobs were created in the wake of Sept. 11. It has been challenged in a lawsuit, filed in federal court in Washington in December by current and retired agents, that accuses the FBI of discriminating against older agents.

The FBI denies any discrimination and is asking a judge to dismiss the case. In a sworn statement filed in court, FBI Deputy Director Timothy P. Murphy wrote that he was “shocked to learn” in 2002 that so few supervisors were applying for new higher-level management positions.

To encourage more applicants, Murphy and another official designed a plan to limit to five years the terms of supervisory special agents, who manage squads of agents in FBI field offices. The policy was enacted in June 2004 after Mueller signed off on it; the limit was extended to seven years in 2008.

FBI officials argue that it has been highly successful, saying that half of the 1,055 supervisors affected have advanced to higher-level positions, while the rest chose to retire, were demoted or resigned.

But one agent said he was “flabbergasted” that Mueller agreed to stay when others have departed.

“Most people think it’s ironic and hypocritical on his part,’’ the agent said. “A lot of really bright people left. It’s a shame.’’