Meanwhile, the White House appeared to rule out an immediate cut in military aid to Egypt over last week's coup, with spokesman Jay Carney telling reporters Monday, "It would not be in the best interests of the United States to immediately change our assistance programs" to Cairo.
Asked repeatedly whether the ouster of Egypt's president and nullification of the constitution was a military coup, Carney said the Obama administration would "take the time necessary" to assess what he called an "incredibly complex and difficult situation" before deciding how to proceed. Under current U.S. law, a coup would stipulate a change in American military aid.
Catherine Ashton, European Union foreign affairs chief, and U.S. State Department spokeswoman Jennifer Psaki called for restraint and urged reconciliation on Monday.
"Dialogue and inclusiveness are the only way forward in speedily restoring a civilian and democratic framework," Ashton said.
Psaki said Washington is focused on "returning stability" and is hoping that Egyptians will unite "in a non-violent and inclusive way."
"We call on the military to use maximum restraint responding to protesters, just as we urge all those demonstrating to do so peacefully," she said.
Elsewhere, in eastern Cairo, Morsy supporters kidnapped two soldiers, state radio reported.
Before the outbreak of violence Monday, more than 30 people had died and 1,400 had suffered injuries since the coup. Egypt's military declared over the weekend it was stepping up security efforts for the demonstrations.
"We also warn against any provocation or clashes with the peaceful demonstrators," the statement said. "Anyone who violates these instructions will be dealt with firmly in accordance with the law."
Top religious figure speaks out
Meanwhile, the grand imam of Egypt's prestigious Al Azhar Mosque called for calm on Monday and urged the release of political prisoners, likely a reference to Muslim Brotherhood members incarcerated in recent days.
Sheikh Ahmad Muhammad Al Tayeb, speaking in an audio played on Egyptian state TV on Monday, also called for all parties to refrain from anything that could lead to bloodshed, passed along his condolences to those who died in Monday's violence and urged the state to protect demonstrators.
Al Tayeb called for an immediate probe of the killings and an immediate announcement of the results. He urged the formation of a committee to achieve national reconciliation and urged the announcement of a timetable for the political transitional period that won't exceed six months. He said media should work toward such reconciliation and not incite.
"I will from now and on retreat to my house, until national reconciliation is achieved and this bloody atmosphere ends," he said. Al Azhar, both the mosque and the university, are influential institutions in the Sunni world.
Morsy supporters vow peaceful protests
Morsy has long been affiliated with the Freedom and Justice Party, the Muslim Brotherhood's political movement. The group promised its protests would be peaceful and accused authorities of planning to send fake bearded men into Cairo's Tahrir Square to incite violence.
"This is so they can claim that the supporters of the elected president and the Islamic groups are attacking the peaceful demonstrators. ... We warn those who play with fire that any sectarian incitement at this critical time will not be in the interests of anyone in our beloved Egypt," the party said in a statement on Facebook.
Tahrir Square will likely attract many people on Wednesday as Ramadan begins in Egypt. Several popular musicians are expected to play, according to state-run EgyNews.
Politics in the midst of chaos
The latest violence came only hours after state television reported that Egypt's interim president had nominated Mohamed ElBaradei as vice president and Ziad Bahaa el Din as prime minister.
Mansour, the interim president, will need to get political consensus before they are appointed.
Presidential spokesman Ahmed Almoslemani stressed on Nile TV there is no specific deadline of when the new government will be announced.
Nile TV had previously reported that he said an announcement would be made within 24 hours.
Earlier, ElBaradei's name had been floated for the office of prime minister, but a swearing-in announced for Saturday didn't happen.
Mahmoud Badr, spokesman for the rebel movement Tamarod, told Egypt's OTV on Sunday that the presidency had tapped ElBaradei to form the new government but then retracted the offer after objections from the conservative al-Nour party.