In Port Said, protesters armed with rocks and shoes forced armored personnel carriers to retreat during a funeral procession for some of those killed in the current violence, The New York Times reported.
Demonstrators called for city residents to ignore President Mohamed Morsi's 9 p.m. curfew.
Police in Cairo fired tear gas at protesters on a bridge that was the site of a battle during the uprising against Hosni Mubarak.
In response to the violence, the Egyptian Cabinet proposed granting the military power to arrest civilians, The Egyptian Independent and MENA reported.
The armed forces would act as police officers, so those arrested would be tried in civilian, rather than military, courts.
The death toll from five days of protests was estimated Monday at 50 by local news media.
"We look to all Egyptians to express themselves peacefully and for all Egyptian leaders to make clear that violence is not acceptable," Carney said. "We welcome serious calls for national dialogue to avoid further violence and define peaceful means to move forward with the political process and building national unity."
Carney said he wasn't aware of whether Obama had spoken with Morsi.
Asked whether the administration condemned any of Morsi's actions as a "cause and effect" of the violence, Carney said, "We look to the government of Egypt to adhere to the right of all Egyptians to have due process. There needs to be a lasting solution to the conflict that we see in Egypt and it has to be a solution that adheres to the rights of all Egyptians."
The 30-day state of emergency, which Morsi announced on state television late Sunday, suspends the normal judicial process and waives most civil rights. Police can investigate, arrest and detain suspects indefinitely without charge.
Opposition to Egypt's emergency law was a key reason for the revolution that ousted Mubarak two years ago. That revolution spurred a democratic shift that led to Morsi's presidential election last June.
Morsi's powerful Muslim Brotherhood organization had been on the receiving end of the much-reviled emergency law under Mubarak.
Morsi said he was using the ousted regime tactic "to stop the bloodbath."
He called weekend street violence "the counterrevolution itself."
"There is no room for hesitation, so that everybody knows the institution of the state is capable of protecting the citizens," he said. "If I see that the homeland and its children are in danger, I will be forced to do more than that. For the sake of Egypt, I will."
He vowed the imposition of the law would not return Egypt to autocracy.
"There is no going back on freedom, democracy and the supremacy of the law," he said.