Supporters of Egypt's ousted President Mohammed Morsi have staged large new protests across the country.
In Cairo, tens of thousands assembled outside the Rabaa al-Adawiya mosque, scene of a weeks-long sit-in.
Crowds backing Mr Morsi's overthrow by the army gathered for a rival rally in Cairo's Tahrir Square, but in smaller numbers.
At least two people were killed during clashes in the Nile Delta city of Mansura, Egyptian media reported.
Meanwhile, the UN's top rights official is pushing Egypt's interim leaders to state why Mr Morsi has been arrested and when he will be put on trial.
Egypt's first freely elected president was ousted on 3 July in what his supporters, many of them members of his Muslim Brotherhood movement, have said was a military coup. He is being held by the army at an undisclosed location.
The spokesman for the UN's High Commissioner for human rights, Navi Pillay, said she had spoken to Egypt's ambassador on 10 July and had written to Cairo for information on how many people were being held with Mr Morsi and the legal basis for their detention.
Ms Pillay also wanted more information on the shooting outside the Republican Guard barracks in Cairo on 8 July in which more than 50 people were killed, said Rupert Coleville.
Each side has accused the other of instigating the violence.
Mr Coleville said a UN team was waiting for permission to travel to Egypt to help with the investigation.
Brotherhood supporters have staged constant protests demanding Mr Morsi's reinstatement, and the movement's leadership had called for a fresh show of strength on Friday, under the banner "Breaking the Coup".
"I've come out to support legitimacy. Not because of President Morsi, but to support legitimacy," one protester told Reuters.
"They stole the vote that I cast in the elections."
Another man, who gave his name as Mohammed, told AFP: "I believe Morsi will return as president, God willing. The people will win in the end."
A spokesman for the Brotherhood, Ahmed Aref, said the turnout had surpassed organisers' expectations.
"This is a peaceful destruction of the coup, and the peaceful will of the people will be achieved and nobody can snatch the will of the people."
A breakaway group of several thousand people attempted to march towards the Republican Guard barracks, where they believe Mr Morsi is being held, but the march was blocked by a cordon of security forces and tanks.
Pro-Morsi protests were also reported in Egypt's second city Alexandria, and in other towns along the Nile Delta.
The website of state-run newspaper Al-Ahram said an Egyptian woman and a 13-year-old boy died in clashes between rival groups in Mansura.
Another report quoting medical sources said three people in Mansura had been killed and another seven injured. The reports could not be verified.
The army says it removed Mr Morsi from office in response to the weeks of protests against him by people who believed he was becoming too authoritarian and moving Egypt towards a more Islamist style of governance.
Pro-army demonstrations have not been as large since the overthrow but organisers, including the Tamarod youth movement, had called for its supporters to turn out again on Friday in Tahrir Square, raising fears of violence if the two sides met.
The Mena state news agency reported small clashes between rival groups outside the Al Al-Azhar mosque before Friday prayers.
In a televised address on Thursday evening, his first since taking office, Interim President Adly Mansour had said Egypt was at a "critical stage" and warned against stoking unrest.
"Some want us to move towards chaos and we want to move towards stability. Some want a bloody path," he said, in a pre-recorded message aired on state TV.
"We will fight a battle for security until the end. We will preserve the revolution."
Military spokesman Col Ahmed Mohammed Ali issued a statement on Thursday warning protesters that "whoever resorts to violence and deviates from peacefulness in Friday's rallies will put his life in danger".
He said violators would be "dealt with decisively according to the law".
Also on Friday, two civilians were killed in an attack on an army checkpoint in the Sinai peninsula, officials said.
The army is trying to contain a surge in violence that has hit Sinai following Mr Morsi's overthrow.
There have been periodic surges in violence on the peninsula as Islamist extremists attempt to take advantage of a security vacuum to gain a foothold.