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.
ElBaradei is well-known as the former head of the U.N. atomic watchdog agency, the International Atomic Energy Agency, and a Nobel Peace Prize winner. He was to appear Sunday in an interview with CNN's Fareed Zakaria but canceled it along with all other media interviews, his office said.