Mullen, who congratulated his good friend and outgoing Chief of Staff Gabi Ashkenazi, said that the relations with the Egyptian army haven't changed and that "maintaining a friendship at such a challenging time is very important."
He said there were many challenges and difficulties in the new situation and that the American military leaders continued to maintain close contact with their counterparts in the Egyptian army.
"There are many challenges which are out there in the future ... We've been so impressed that they have supported their people," said Mullen.
"We've got a very strong relationship with the Egyptian military ... and we continue to stay in very close touch with our counterparts in the Egyptian military."
Mullen said he had met with Prime Minister Benjamin Netanyahu and discussed "the current challenges".
He also voiced admiration for the way Egypt's army had peacefully handled the shift of power in the country.
"I think they have handled this situation exceptionally well ... it's been done peacefully, and we have every expectation that that will continue."
Meanwhile Monday, Egypt's military delivered an ultimatum to dozens of committed protesters in Tahrir Square, nerve-centre of a movement that toppled Hosni Mubarak, to leave and let life get back to normal or face arrest.
Some protesters insisted on staying in Cairo's central square, determined to see through their demands for civilian rule and a free, democratic system.
"We have half an hour left, we are cordoned by military police," protester Yahya Saqr told Reuters. "We are discussing what to do now," he said, adding that a senior officer "told us we have one hour to empty the square or we will be arrested."
Protest leaders say Egyptians will demonstrate again if their demands for radical change are not met. They plan a huge "Victory March" on Friday to celebrate the revolution, and perhaps remind the military of the power of the street.
Reuters contributed to this report
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