Under prodding from a senator Thursday, Attorney General Eric H. Holder Jr. hedged on just how long he intends to remain head of the Justice Department.

Holder has been under fire for most of his tenure, which began when President Obama took office in 2009. But the criticism has increased in recent weeks over controversies involving the department’s seizure of phone and e-mail records from the Associated Press and Fox News. Last month, House Republicans accused Holder of giving false testimony on the seizures, and some called for his resignation.

The pressure seems to have taken a toll on Holder. At the start of the hearing before a Senate Appropriations subcommittee, Sen. Richard C. Shelby (R-Ala.) sharply criticized the attorney general’s leadership and asked him when he was going to leave.

“I’m interested to know what criteria you will use to determine whether you can continue to lead the department,” Shelby said. “In other words, what’s the tipping point here?”

“The tipping point might be fatigue,” Holder answered. “You get to a point where you just get tired.”

Aides close to Holder later said he was joking and that he is not fatigued or tired.

Holder said he will meet with Obama after he accomplishes the goals that he has set for himself.

“I will sit down with the president, and we’ll talk about a transition to a new attorney general,” Holder said. “I think that change is frequently a good thing for an organization, a new perspective. . . . This has been the honor of my professional life, to serve as attorney general. But I also have such respect for the Department of Justice that I want to make sure that it operates at peak efficiency and that new ideas are constantly being explored.”

He added, “And when the time comes for me to step aside for my successor, I will do so.”

Although the hearing was called to discuss the department’s budget, questioning ranged across several topics. Among them were the revelations that the National Security Agency, under a secret court order, is collecting the telephone records of millions of American customers of Verizon, one of the nation’s largest phone companies.

“Could you assure us that no phones inside the Capitol were monitored of members of Congress that would give a future executive branch . . . unique leverage over the legislature?” asked Sen. Mark Kirk (R-Ill.). He also asked for assurance that the phone records of Supreme Court justices had not been seized.

“There has been no intention to do anything of that nature, that is, to spy on members of Congress, to spy on members of the Supreme Court,” Holder replied.

But he said it was inappropriate for him to discuss the issue outside a classified briefing.

Sen. Lindsey O. Graham (R-S.C.) offered a different point of view, saying he was “glad” that the NSA is collecting phone records.

“I’m a Verizon customer,” Graham said. “It doesn’t bother me one bit for the National Security [Agency] to have my phone number, because what they’re trying to do is find out what terrorist groups we know about and individuals, and who the hell they’re calling.”

Holder’s tenure came up toward the end of the hearing, when Graham asked him about the effects of sequestration on the Justice Department.

“Since January of 2011, I’ve put a hiring freeze in place,” Holder said. “We lost 2,400 people. We’ve lost about 600 prosecutors. . . . These are people who have left the Department of Justice and who have not been replaced.”

He said that if financial help does not arrive, FBI agents will be taken off the streets and prosecutors will be absent from courtrooms.

“Whoever the attorney general is a year, two years from now, you’re going to see reduced numbers with regard to prosecution,” Holder said.

Holder has told reporters that he is not planning to step down now, but some of his advisers have speculated that he will leave by the end of the year. Among the names that come up as possible successors are Massachusetts Gov. Deval L. Patrick (D), a former assistant attorney general who is close to Obama, and Homeland Security Secretary Janet Napolitano.

Patrick said Thursday, “I have the only job in public life I want, and I’m going to stay here and finish it.” His term ends in 2014.

Julie Tate contributed to this report.