Secretary of State Hillary Rodham Clinton has told President Obama that she will stay in office until her successor is confirmed, but said in an interview that “this is not an open-ended kind of time frame.”

“It’s really still my same time frame,” Clinton said, reiterating her intention to step down after one term even if Obama is reelected. “I’m aiming to leave shortly after the inauguration; that’s my plan. But I haven’t been able to sit down and talk to the president yet because he’s trying to win an election, which hopefully will be finalized shortly. And then we will talk through how to do the transition.”

Clinton was responding to news reports that she was considering staying on longer to deal with matters related to the Sept. 11 attack on the U.S. diplomatic mission in Benghazi, Libya, which killed U.S. Ambassador J. Christopher Stevens and three other Americans.

The reports had set off a minor flurry of speculation that Clinton — among the most popular members of Obama’s Cabinet and still the most-rumored Democratic presidential candidate for 2016 — might be willing to remain for a partial or full second term if Obama is reelected. She has said repeatedly that she would serve only one term.

White House press secretary Jay Carney seemed happy to leave that door open while Obama is in a tough reelection fight with Republican Mitt Romney and might benefit from the possibility of Clinton staying on board.

“I think you heard the president say very explicitly what an excellent job she’s done as secretary of state and how he would, of course, like her to stay on,” Carney told reporters aboard Air Force One on Thursday. “I can’t say it better than the way the president said it last night in terms of his interest in having her stay if she could be persuaded.”

But in an interview later Thursday, Clinton underlined that she is unlikely to be persuaded.

“I’m not really open to staying longer, but I also know that we have to be conscious of the work that has to be done,” she said. “And again, I’ll have to talk to the president.”

Clinton was a surprise choice for the job after her bitter fight with Obama for the Democratic nomination in 2008. Clinton has said she will not run for president in 2016, but speculation remains rampant that she could be persuaded to change her mind.

If Obama beats Romney, the idea that Clinton might linger beyond Inauguration Day is not unusual. Cabinet members often remain in office until a successor is confirmed by the Senate.

Gen. Colin L. Powell, President George W. Bush’s first secretary of state, had cleared out his office and removed portraits from the walls the day before Bush’s second inauguration in January 2005. But the Senate, where members remained angry over the Iraq war, did not confirm Condoleezza Rice as his replacement for a week, and Powell remained in place until then.

One of the people mentioned to succeed Clinton, Susan E. Rice, the U.S. ambassador to the United Nations, has been damaged by the political fallout from the Benghazi attack. Rice delivered the administration’s message five days after the attack on network talk shows, which raised her public profile ahead of a possible nomination. But her suggestion that the attack was partially rooted in protests over an anti-Islam video was quickly discredited.

Clinton said the decision on a successor belongs to the president. She did talk about how the attack in Benghazi has affected her thinking, describing the “inherent tension” between keeping diplomats safe and engaging more with people beyond the walls of embassies, an idea she has championed.

Besides constantly taking stock of new threats, Clinton said the State Department is focusing on the host country’s responsibility for protecting diplomatic missions.

“What if a country can’t do that or refuses to do that?” she said. “That does introduce a new level of analysis that we have been working on for months. And what happened in Benghazi just throws that into high relief.”

Karen DeYoung and Anne Gearan contributed to this report.