Cheney's comments came a day after President Barack Obama pressed Mubarak to consider his legacy and exit office in a way that would give his country the best chance for peace and democracy.
Cheney said the U.S. should take measured steps in public, and suggested that too much pressure could backfire.
"There is a reason why a lot of diplomacy is conducted in secret. There are good reasons for there to be confidentiality in some of those communications. And I think President Mubarak needs to be treated as he deserved over the years, because he has been a good friend," Cheney said at an event commemorating the centennial of President Ronald Reagan's birth.
Cheney noted it can be difficult for some foreign leaders to act on U.S. advice "in a visible way" without appearing compromised in their own countries.
"The bottom line is, in the end, whatever comes next in Egypt is going to be determined by the people of Egypt," Cheney added.
Cheney, looking markedly thinner than during his days in Washington and sitting throughout his remarks, said Mubarak helped the U.S. get military aircraft into the region in the 1991 Gulf War, and committed troops to fight alongside U.S. forces in the liberation of Kuwait.
"He's been a good man, a good friend and ally to the United States," Cheney said. "We need to remember that."
As huge protests continued Friday, Obama said discussions have begun in Egypt on a turnover of the government, and he called for a "transition period that begins now."
"We want to see this moment of turmoil turned into a moment of opportunity," Obama said in Washington. He did not explicitly call for Mubarak to step down immediately, but U.S. officials said the administration has made a judgment that Mubarak has to go soon if the crisis is to end peacefully.
Asked about a possible outcome in Egypt, Cheney said, "I don't know."
"There comes a time for everybody when it's time to hang it up and move on," he said, but added, "That's a decision only the Egyptians can make."
Saturday's event was sponsored by the Young America's Foundation, which was founded to promote conservative ideas on college campuses and purchased Reagan's former ranch in 1998.
Sarah Palin addressed the group Friday.