Protesters moved towards the military intelligence building, the interior minister's home and an airport road.

They are continuing to stage large sit-ins in the capital to call for Mr Morsi's reinstatement.

EU foreign policy chief Catherine Ashton is in Cairo for talks.

She is to meet leaders of Mr Morsi's Muslim Brotherhood, the head of the Egyptian armed forces, Gen Fattah al-Sisi and interim President Adly Mansour.

In a statement, she said she would push for a "fully inclusive transition process, taking in all political groups, including the Muslim Brotherhood".

At the moment, there is little sign that outside voices are being heard, or that mediation initiatives by local figures are making headway, says the BBC's Jim Muir in Cairo.

Mr Morsi was replaced by the military on 3 July after large demonstrations against his rule.

The Muslim Brotherhood continues to demand his return to office, with a large protest camp outside the eastern Rabaa al-Adawiya mosque and further west near Cairo University.

In the worst violence seen since Mr Morsi was deposed, more than 70 people were killed in clashes with the security forces on Saturday.

The security forces have been accused of using excessive force, but the interior ministry says protesters used firearms.

In a further warning, the National Defence Council, which includes members of the interim government and the military, warned on Sunday of "firm and decisive" action against protesters who go beyond peaceful demonstration.

On Monday, Muslim Brotherhood supporters say they staged three marches.

One targeted the headquarters of military intelligence. Muslim Brotherhood spokesman Gehad el-Haddaf told the BBC there was no intervention by the military and no confrontation.

He said the march "circled the building for a good 10 to 15 minutes with a lot of chants of 'down with the coup'". However, one report suggests many turned back before reaching the building.

Mr Morsi supporters say they are planning a further large demonstration on Tuesday - they have called a "million-man march".

On Sunday, Egypt's new Foreign Minister, Nabil Fahmy, urged restraint, telling the BBC that all sides "need to stop inciting violence and using violence".

Mr Fahmy said his government would like to move forward "but that requires cessation of violence and incitement".

Responding to criticism that some members of the army and police had gone too far on Saturday, he said: "If you have people shooting each other on both sides then you're obviously going to have to casualties."

Interior Minister Mohamed Ibrahim has repeatedly warned that the camp outside the mosque would be dispersed "soon".

Thousands of Morsi supporters, some with their families, have made the mosque the focal point of their round-the-clock protest.

Speakers from the pro-Morsi Muslim Brotherhood, whom the protesters support, say they will not back down from their demands.

Mr Morsi has been formally remanded in custody at an undisclosed location, according to a judicial order.

He has been accused of the "premeditated murder of some prisoners, officers and soldiers" when he and several Muslim Brotherhood leaders were freed during a breakout at a Cairo prison in January 2011.

He is alleged to have plotted attacks on jails in the uprising that overthrew President Hosni Mubarak.

Mr Morsi is also accused of conspiring with the Palestinian militant group Hamas, which governs the Gaza Strip and has strong links with the Muslim Brotherhood.