The Egyptian government removed Mohamed Morsi from power July 3. A candidate from the Muslim Brotherhood's political arm, he was the first Egyptian president ever elected by a democratic vote.
The Muslim Brotherhood pressed visiting European leaders last week to characterize the ouster as a military coup. Western governments have been reluctant to describe it as such because of legal issues related to foreign aid.
The British government last week revoked export licenses for some military equipment to Egypt because of political violence. Egyptian news agency al-Ahram reported fighting broke out Monday in Cairo between pro- and anti-Morsi demonstrators.
The Muslim Brotherhood issued a statement Sunday saying the will of the Egyptian people should be respected.
"The Brotherhood is working to achieve social peace, rejects any foreign interference in the affairs of Egypt, seeks to maintain the national security of the homeland and the Arab world, and respects the sanctity of all Egyptian blood," it said. "We work in the light of Koranic directives."
Morsi was criticized for failing to address ongoing economic woes and for favoring Islamic political ideologies while in office. The Muslim Brotherhood has rejected offers made so far by interim political leaders.