The U.S. urged "all Egyptians to resolve their differences over these important issues peacefully and through democratic dialogue," she said.
Amnesty International, the London-based rights group, said Morsi's new powers "trample the rule of law and herald a new era of repression."
Morsi aide Samer Marqous, a Coptic Christian, resigned to protest the "undemocratic" decree.
"Morsi's decision means dictatorship. He creates the law, passes the law, and oversees the law," said Manal Tibe, an activist who was a member of the assembly writing the new constitution until she withdrew earlier this year to protest the Islamists' domination of it. "He is the state and the state is him."
Mohamed ElBaradei, Egypt's most prominent reformer and a Nobel Peace laureate, warned that Morsi was making himself a "pharaoh" and appealed to him to withdraw the decrees "before the polarization and aggravation of the situation increases."
In his decrees, Morsi ruled that any decisions and laws he has declared or will declare are immune to appeal in the courts and cannot be overturned or halted. He also barred the judiciary from dissolving the upper house of parliament or the assembly writing the new constitution, both of which are dominated by the Brotherhood and other Islamists.
The edicts would be in effect until a new constitution is approved and parliamentary elections are held, which are not expected until the spring.
Morsi also declared his power to take any steps necessary to prevent "threats to the revolution," public safety or the workings of state institutions. Rights activists warned that the vague — and unexplained — wording could give him even greater authority than Mubarak had under emergency laws throughout his rule.
In his speech, Morsi warned of "weevils eating away at the nation of Egypt," and pointed to old regime loyalists he accused of using money to fuel instability and to members of the judiciary who work under the "umbrella" of the courts to "harm the country."