Kurtzer told students in a talk at Princeton University that a similar gesture by Mubarak several days ago may have been enough to quiet the situation.
But the intensity of protests may have changed what demonstrators want, Kurtzer said.
Mubarak announcing last week that he would leave office but stay on for a transition might have been "an ideal outcome," Kurtzer said.
"That ideal outcome may not be available today," he said.
Kurtzer said he's known Mubarak since before he took office 30 years ago. The diplomat, who was ambassador in Egypt from 1997 to 2001 and to Israel from 2001 to 2005, said Mubarak modernized his nation's infrastructure and economy even as his overriding goal seemed to be to maintain the status quo.
"I've often joked, and it's true," Kurtzer said, "the perfect day for Mubarak is a day in which nothing happens."
During his time in office, Mubarak also kept intact a peace treaty between Egypt and Israel and was a stable partner for the United States, Kurtzer said.
The leadership that follows might be more complicated, Kurtzer said.
One of the groups on the edges of the protests has been the Muslim Brotherhood, which Kurtzer says might not be friendly to the U.S. interests.
"The Muslim Brotherhood since its founding in 1928 has had one single goal, and that is to transform Egypt into a Muslim state - and once that is achieved, to turn the Middle East into a pan-Arab Islamist state," Kurtzer said.
He said that group's alignment with pro-democracy protesters doesn't mean it's a pro-democracy group.
"The Brotherhood has tactical flexibility, but let none of us be misled about their strategic goal, which has not changed one iota."
The former ambassador said the U.S. has mostly done well at maintaining a delicate balance between encouraging democracy in Egypt and standing behind an ally.
He said the Obama Administration's one misstep came last week when it suggested that the U.S. might re-evaluate its aid to Egypt.
But he said it's not public statements that will help the U.S.
"The degree to which we can be influential depends more on what we're doing privately," he said.
He said he expects that the protests will lead, eventually, to meaningful economic and political reforms in Egypt.
If they don't, he said, "One could only surmise that the demonstrators would find their way back to the streets."