Her emphasis on a deliberate process was repeated by Mrs. Merkel and Mr. Cameron. Mrs. Merkel mentioned her past as a democracy activist in East Germany, recalling the impatience of protesters after the fall of the Berlin Wall in 1989, to immediately join democratic West Germany. But the process took a year, and it was time well spent, she said.

“There will be a change in Egypt,” Mrs. Merkel said, “but clearly, the change has to be shaped in a way that it is a peaceful, a sensible way forward.”

Mrs. Clinton highlighted fears about deteriorating security inside Egypt, noting the explosion at a gas pipeline in the Sinai Peninsula, and uncorroborated news reports of an earlier assassination attempt on Mr. Suleiman.

American officials did not confirm that an assassination attempt had taken place. But Mrs. Clinton referred to reports of the attempt and said it “certainly brings into sharp relief the challenges we are facing as we navigate through this period.”

In a statement, the Egyptian government said there had been no assassination attempt, but added that on Jan. 28 a car in Mr. Suleiman’s motorcade was struck by a bullet fired by “criminal elements.”

At the same Munich meeting on Saturday, Frank G. Wisner, the former ambassador President Obama sent to Cairo to negotiate with Mr. Mubarak, appeared to take an even softer line on the existing government, saying that the United States should not rush to push Mr. Mubarak out the door. He said Mr. Mubarak had a critical role to play through the end of his presidential term in September.

“You need to get a national consensus around the preconditions of the next step forward, and the president must stay in office in order to steer those changes through,” Mr. Wisner said.