The clashes have so far produced a death toll of more than 500.
Brotherhood members on Thursday torched government headquarters in Giza, rallying for support following military raids Wednesday on Brotherhood protest camps in Giza and Cairo.
Egypt's military-backed government declared a state of emergency Wednesday and imposed a curfew in Cairo, Giza and eight other provinces.
Interim vice president Mohamed ElBaradei resigned Wednesday, saying in a letter to leaders that he didn't want to be responsible for such violence when there are more "peaceful" options.
"As you know, I saw that there were peaceful ways to end this clash in society, there were proposed and acceptable solutions for beginnings that would take us to national consensus. It has become difficult for me to continue bearing responsibility for decisions that I do not agree with and whose consequences I fear. I cannot bear the responsibility for one drop of blood."
Interim president Adly Mansour has "tasked the armed forces, in cooperation with the police, to take all necessary measures to maintain security and order and to protect public and private property and the lives of citizens."
In the dispersal of the sit-ins of Rabaa and Nahda, Egypt's Interior Ministry said more than 500 pro-Morsi protesters were arrested nationwide, mostly for possession of arms including automatic weapons and large amounts of ammunition.
U.S. Secretary of State John Kerry has urged restraint, saying "Egyptians inside and outside of the government need to take a step back" to avoid further violence.
"We also strongly oppose a return to a state of emergency law, and we call on the government to respect basic human rights, including freedom of peaceful assembly and due process under the law. And we believe that the state of emergency should end as soon as possible," Kerry said.