Another administration official said the unrest was “going to have a really negative effect” on all the initiatives but added that much remained unclear and that the focus was on damage control.

Regardless of the challenges, and possible setbacks to vital negotiations, senior American officials said on Sunday that the mission had to go on. “This is not the time to decide that we’re done here,” the American ambassador in Kabul, Ryan C. Crocker, said in an interview on CNN. “We have got to redouble our efforts. We’ve got to create a situation in which Al Qaeda is not coming back.”

Secretary of State Hillary Rodham Clinton expressed regret for the burning of the Korans but said it should not derail the American military and diplomatic effort in Afghanistan. “We are condemning it in the strongest possible terms,” she said in Rabat, Morocco, “but we also believe that the violence must stop, and the hard work of trying to build a more peaceful, prosperous and secure Afghanistan must continue.”

Another administration official said, however, that there was recognition that the commitment was most likely to carry a greater political cost. “There is no less a commitment to a long-term relationship with Afghanistan,” the official said. “But is there a concern now that many will question the need to stay? Yes — especially in an election year.”

A leading Republican candidate for president did appear to strike a more measured tone on Sunday in speaking about the crisis in Afghanistan while urging that the United States stay on its course.

Mitt Romney, speaking to Fox News, said: “It’s obviously very dangerous there, and the transition effort is not going as well as we’d like to see it go. But certainly the effort there is an important one, and we want to see the Afghan security troops finally able to secure their own country and bring our troops home when that job is done.”

He did, however, reiterate his opposition to the administration’s setting a public timetable for drawing down American forces in Afghanistan. And he and his main rival in the Republican field, Rick Santorum, on Sunday continued their harsh criticism of Mr. Obama’s apology for the Koran burnings.