Frank Wisner, who was dispatched to Cairo on Monday, said he is increasingly hopeful that Egypt can manage a peaceful and orderly transition to democracy.
He said by video link from New York to a security conference in Munich that "the flexibility is there, the imagination is there."
Wisner, a former ambassador to Egypt, said that the president's departure would under the current constitution trigger elections in two months under conditions that are "broadly unacceptable" to protesters.
"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," Wisner said. "I therefore believe that President Mubarak's continued leadership is critical - it's his opportunity to write his own legacy."
Mubarak has said that he won't seek another term in office but demonstrators are demanding that he go now.