“They took a little while to catch up, but by Sunday morning they understood that it was over, and since then, they’ve understood how to make it happen,” said Martin S. Indyk, the director of foreign policy at the Brookings Institution.

Still, administration officials were grappling with their public message versus their private message. Senior officials say that as Mr. Wisner traveled to Egypt, Obama officials in Washington were working on his message to Mr. Mubarak: to announce that he would not run for re-election (he did that), and to promise that his son would not run for election (he did not do that).

“No one wanted it to seem as if we were pushing him out,” one administration official said. “That would not serve American interests. It was important for President Mubarak to make the decision.”

Two hours after Mr. Wisner’s plane left Andrews Air Force Base, White House officials sent an e-mail to more than a dozen foreign policy experts in Washington, asking them to come in for a meeting on Monday morning. “Apologies for the short notice in light of a very fluid situation,” the e-mail said.

The Roosevelt Room meeting, led by Benjamin Rhodes, the deputy national security adviser for strategic communications, and two other National Security Council officials, Daniel Shapiro and Samantha Power, examined unrest in the region, and the potential for the protests to spread, according to several attendees.

Significantly, during the meeting, White House staff members “made clear that they did not rule out engagement with the Muslim Brotherhood as part of an orderly process,” according to one attendee, who like others interviewed for this article spoke on condition of anonymity because he did not want to talk publicly about the meeting. The Muslim group had been suppressed by Mr. Mubarak, and Bush administration officials believed it was involved in terrorist activities. It renounced violence years ago.

Several times, two other attendees said, White House staff members said that Mr. Obama believed that Egyptian politics needed to encompass “nonsecular” parties: diplomatic-speak for the Muslim Brotherhood.