Egypt’s interim president, Adly Mansour, has said that a plan for a return to civilian government after the army’s removal of Islamist President Mohamed Morsi was on track despite “challenges” and that emergency law should be lifted soon.

His comments were broadcast just after thousands of Islamists took to the streets in towns and cities across Egypt late on Tuesday evening to denounce the new military-backed rulers and demand Morsi’s return – their second show of mass support in four days.

The interim government has launched a furious crackdown on Morsi’s Muslim Brotherhood since toppling Egypt’s first freely elected president on July 3, following huge protests.

It has accused the group of terrorism, sent its top leaders to trial on charges of inciting violence or murder and killed hundreds of Islamists demanding his reinstatement, most of them when two Cairo protest vigils were smashed on August 14.

Mansour said in an interview with state television that his decision to announce emergency law that day had not been easy, but “terrorism and the vicious war that was being waged by some of the extremists made it crucial.”

If a “gradual improvement in security” continued, the state of emergency should end as planned in mid-September, he said.

Morsi and other Muslim Brotherhood leaders face trial

Mansour also said a “road map” back to democratic rule, under which the constitution is to be amended, followed by parliamentary and presidential elections early next year, remained on track: “God willing, we will commit ourselves to the timeframe in the coming stages.”

“There are no alterations on the priorities of the plan (road map), even though there are some challenges facing us.”

Although the army-backed interim government has begun to revive the political security apparatus that was shelved, but not dismantled after the 2011 revolt that overthrew Hosni Mubarak, Mansour said there would be no return to the days of political police.

“The role of the security apparatus of Egypt is now limited to protecting security and protecting the people ... in terms of political issues, there is no longer a role in that. That was a period that Egypt passed through and it will not return ... I assure you of that.”

Although the crackdown on the Brotherhood has taken some of the sting out of the anti-government protests, the well organised million-member group has shown it can still mobilise supporters countrywide.

Shortly before the interview was aired, marchers turned out in cities in the Nile Delta, in Upper Egypt, along the Suez Canal, as well as in the capital, to mark exactly two months since Morsi was toppled.

There were no immediate reports of violence at Tuesday’s marches, held under the slogan “The Coup is Terrorism” – a reference to the government’s portrayal of its campaign to crush the Brotherhood as a fight against Islamist terrorism.

In Cairo’s Nasr City, near Mansour’s presidential palace, hundreds of marchers waving Brotherhood flags chanted “Revolution, revolution, the revolution will continue!” and “Down, down with military rule!” Some carried pictures of “martyrs” killed in the government’s crackdown, while others stood chanting next to an armoured vehicle.

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