Egypt's military authorities have launched a crackdown against Muslim Brotherhood members and issued arrest warrants on 300 Islamist affiliates wanted for incitement to violence.

The Egyptian prosecutor's office ordered the arrest of the organisation's leader, Mohamed Badie, and his deputy Khairat el-Shater, who was the group's prime candidate to run in the 2012 presidential election. He had to step down because of past convictions, paving the way for Morsi's candidature.

Shater and Badie were accused of inciting violence in which at least eight people were killed in the widespread protests that led to the coup.

The development came after the National Salvation Front, the main alliance of liberal and leftist parties, expressed its support for the right of Islamist parties to be included in the political process.

"We confirm our strong belief in the right of all political groups to express their opinions freely, and to form their own political parties. We reject excluding any party, particularly political Islamic groups," the group said.

"What Egypt is witnessing is not a military coup by any standards. It was a necessary decision that the armed forces' leadership took to protect democracy, maintain the country's unity and integrity, and restore stability."

The head of Egypt's constitutional court, Adli Mansour, has been sworn in as interim president after the military deposed Mohamed Morsi in the country's second revolution in two years.

Mansour said he wanted all sides represented in the transition to the next elected government.

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