Clinton urged "intensive dialogue" among all sides "in order to ensure that there is a clear path for them to be following and that the Egyptian people get what they protested for and what they voted for, which is a fully elected government."
The U.S. secretary of state made the comments in the middle of a marathon trip to Europe, Asia and the Middle East, where she plans to visit Cairo on July 14, becoming the senior-most U.S. official to visit since Mursi was sworn in on June 30.
Clinton said that democracy was about more than elections.
"It is about creating a vibrant, inclusive political dialogue, listening to civil (society), having good relations between civilian officials and military officials, where each is working to serve the interests of the citizens," she said.
(Reporting by Arshad Mohammed; Writing by Alan Raybould; Editing by Jonathan Thatcher)