Egyptian police fired tear gas on crowds protesting in Cairo's Tahrir Square, the home of the revolution that ended Hosni Mubarak's 30-year reign over Egypt last year.
Protesters chanted slogans calling for Morsi's resignation after he issued a decree last week giving him sweeping powers in a move said to be a temporary one to facilitate constitutional developments.
Amr Moussa, a former Arab League secretary-general and presidential contender, told Germany's Der Spiegel that the Egyptian president issued his decree "out of the blue" in direct contradiction to Egypt's emerging democracy.
"Some of the decrees issued by the president are extremely problematic and grant him a worrying amount of power," he said.
Morsi, the candidate from the Muslim Brotherhood's Freedom and Justice Party, was elected in June in the first democratic vote in the country's history.
Moussa told the German news magazine that he formed the National Salvation Front last weekend as a formal opposition movement.
"What is currently taking place in Egypt represents a grave danger to the process of democratization in our country," he said. "Public opinion has never been as polarized as it is today."
News agency Egyptian Independent reports that Egyptian leaders expect to complete the final draft of the post-revolution constitution by late Wednesday.