Tensions have been running high since dozens were killed at a pro-Morsi rally in Cairo on Saturday.
Khaled al-Khateeb, the head of the central administration of Egypt's emergency services, on Monday revised the toll in the clashes up to 81, not including a police officer who died of his wounds.
The health ministry had earlier given a toll of 72.
The White House "strongly" condemned the recent violence, and urged the military-backed interim government to respect the rights of demonstrators.
Monday night's marches began around 2100 GMT, after backers of deposed Islamist president Mohamed Morsi broke their Ramadan fast.
Groups moved from their key sit-in site by the Rabaa al-Adawiya mosque in Cairo towards the interior ministry and two other security forces buildings.
Thousands of demonstrators, men and women chanted slogans against army chief General Abdel Fattah el-Sisi, who led the coup against Morsi.
Hamza Sarawy, a spokesman for the Muslim Brotherhood's political party, said protests would be peaceful and demonstrators would return to their sit-in afterwards.
"We have no plans for any violence and we are not going to sit in, we will march there and then back" to Rabaa al-Adawiya mosque, he said.
Earlier the Anti-Coup Alliance of Islamist groups protesting against Morsi's ouster also called for a massive turn-out on Tuesday.
"We... call for a million person march under the banner of 'Martyrs of the Coup' on Tuesday," they said in a statement.
They urged Egyptians "to go out into the streets and squares, to regain their freedom and dignity -- that are being usurped by the bloody coup -- and for the rights of the martyrs assassinated by its bullets".
The calls raised the possibility of fresh confrontations after the National Defence Council warned protesters "not to exceed their rights to peaceful, responsible expression of their opinions".
The council said demonstrators would face "decisive and firm decisions and actions in response to any violations".
The military issued its own warning overnight, urging protesters not to "approach military facilities or units, help us to protect your safety," it said.
With tensions rising, EU foreign policy chief Catherine Ashton decided to extend by one day a visit that began late Sunday.
She has already met interim president Adly Mansur, vice president for international affairs Mohamed ElBaradei and army chief General Abdel-Fattah al-Sisi.
On Monday night, she also met representatives of the pro-Morsi coalition, but was not expected to comment on her discussions until Tuesday.
"There were no initiatives presented by Ashton or us, she just heard updates on the situation since her last visit," Mohamed Ali Bishr, a pro-Morsi delegation member said.
The bloodshed in the Arab world's most populous nation has sparked mounting international concern, and Washington on Monday "strongly" condemned the violence.
"The United States strongly condemns the bloodshed and violence," the White House said in a statement, urging the interim government to respect demonstrators' rights.
A group of Egyptian NGOs issued a statement on Monday calling for Interior Minister Mohamed Ibrahim to be sacked for what it called Saturday's "massacre".
"The interior minister should be dismissed and held accountable for his actions," the groups wrote. But they also urged Morsi supporters to "take action to persuade their colleagues and leaders to renounce" violence.
In its first comments on the bloodshed, the interim presidency said Sunday that it was "saddened" by the deaths, but dubbed the protest area where they occurred a "terror-originating spot".
A crackdown on Morsi supporters continued Monday, with the arrest of the president and vice president of the moderate Islamist Wasat party, which has protested the July 3 coup.
Morsi is being held at an undisclosed location on suspicion of crimes relating to his escape from prison during the 2011 uprising that overthrew president Hosni Mubarak.
In the Sinai Peninsula meanwhile, a security source said two policemen were killed in separate shooting attacks in El-Arish.
And in Cairo, 15 people were killed in a brawl between street vendors and shop owners over space -- including 13 who died in a fire.
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