Egypt's cabinet is set to discuss the crisis in the country, where hundreds have died in clashes in recent days.
The interim prime minister has put forward a proposal to legally dissolve the Muslim Brotherhood.
Its members are key supporters of Mohammed Morsi, whose ousting as president sparked Egypt's stand-off.
The interim government is doing all it can to prevent the regrouping of the Brotherhood, which it blames for the bloodshed.
Overnight, television pictures showed protesters on the streets of Egypt's second largest city, Alexandria, and in Helwan and Minya to the south of Cairo, in defiance of an overnight curfew.
On Saturday Egypt's security forces cleared the al-Fath mosque in Cairo after a long stand-off with Muslim Brotherhood supporters barricaded inside.
The confrontation at the al-Fath mosque continued for most of Saturday – with exchanges of gunfire between protesters and security forces, who were cheered on by crowds outside.
The Brotherhood has called for daily demonstrations since a crackdown on its protest camps in Cairo on Wednesday left hundreds of people dead. Further clashes on Friday killed at least another 173 people across the country.
The interim government is acting quickly to try to undermine the capacity of the Muslim Brotherhood to mount further resistance to it.
On Saturday, the interior ministry said 1,004 Muslim Brotherhood members had been detained in raids across the country, with bombs, weapons and ammunition seized.
The Brotherhood was quoted as saying sons and daughters of leadership figures had been targeted in an attempt to gain leverage over the organisation.
Another figure detained was Mohammed al-Zawahiri – brother of al-Qaeda leader Ayman al-Zawahiri – whom officials said had planned to support the Brotherhood supporters previously holed up in the al-Fath mosque.
Multiple figures in the interim government have said they are engaged in a battle against the forces of "terrorism".
Since Mr Morsi's removal on 3 July, Brotherhood members and supporters have attacked churches, police stations, and the homes and businesses of Christians, hardening public attitudes against the group. But many supporters of the army say the Western media has overlooked such attacks.
"There will be no reconciliation with those whose hands have been stained with blood and who turned weapons against the state and its institutions," interim Prime Minister Hazem Beblawi told reporters.
His proposal to dissolve the Brotherhood raises the stakes in the struggle for the control of Egypt, says the BBC's Bethany Bell in Cairo.
If it is acted upon, it could force the group underground and allow its sources of funding to be targeted.
Despite being closely allied to deposed President Morsi's government, the Brotherhood has always technically been a banned organisation – dissolved in 1954 by Egypt's military rulers. But it recently registered itself as a non-governmental organisation.
In a statement, a spokesperson for the UN Secretary-General Ban Ki-moon said he "strongly condemns attacks on churches, hospitals, and other public facilities, which he finds unacceptable.
"The secretary-general believes that preventing further loss of life should be the Egyptians' highest priority at this dangerous moment."
Mr Ban urged both sides to show "maximum restraint" and for authorities to "adopt a credible plan to contain the violence and revive the political process hijacked by violence. Time is of the essence."
But a political solution to the crisis seems very distant, our correspondent says.
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