In what is seen as a trial of strength, supporters of Mohammed Morsi filled the streets around a mosque in Cairo to condemn his removal by the army.
Army supporters converged on Tahrir Square, just a few miles away.
The detained ex-leader has been formally accused of conspiring with the Palestinian militant group Hamas.
Early on Saturday, Interior Minister Mohammed Ibrahim said the sit-in protest by Morsi supporters at the Rabaa al-Adawiya mosque in Cairo would be "brought to an end soon and in a legal manner".
He gave no details but said local residents had complained about the encampment.
Earlier this week, army chief Gen Abdel Fattah al-Sisi urged people to take to the streets to give the military a mandate for its intervention in removing Mr Morsi and establishing an interim government.
Since Mr Morsi, the country's first democratically elected president, was ousted on 3 July, dozens of people have died in clashes between his supporters and opponents.
Militants have also staged deadly attacks in the Sinai peninsula. Unconfirmed reports spoke of an attack on security forces in the town of Sheikh Zuwayid on Friday.
'Sisi out!'Some of the injured reportedly suffered gunshot wounds in the fighting, which began when Morsi and Sisi supporters confronted each other after Friday prayers.
As darkness fell, street battles appeared to be continuing as police struggled to contain the violence with tear gas.
In Cairo, 11 people were injured in clashes between rival groups in the Shubra district, security sources say. The violence appears to have involved stone-throwing.
Tens, if not hundreds, of thousands of army supporters have gathered on Tahrir Square, the BBC's Jim Muir reports from the scene.
The square is full of people in boisterous, jubilant mood, saluting low-flying army helicopters with green laser pens and letting off fireworks, he says.
A huge crowd of Morsi supporters filled streets around Cairo's Rabaa al-Adawiya mosque, where they have been holding a sit-in protest.
"Sisi out! Morsi is president! Down with the army!" they chanted.
Correspondents say the mood among the Morsi supporters around the mosque has been calm and stewards have been searching demonstrators to ensure no weapons are brought to the rally.
Accusations 'ridiculous' Mr Morsi is being held over allegations of links with Palestinian militants Hamas and plotting attacks on jails in the 2011 uprising that overthrew President Hosni Mubarak, it was announced earlier on Friday.
He is to be questioned for an initial 15-day period, a judicial order said.
The order issued on Friday is the first official statement on Mr Morsi's legal status since he was overthrown and placed in custody at an undisclosed location.
The judicial order says the former president is suspected of conspiring with Hamas, which governs the Gaza Strip and has strong links with Mr Morsi's Muslim Brotherhood, during the uprising against Mr Mubarak.
He is accused of colluding with the Palestinian group to storm police stations and jails, "setting fire to one prison and enabling inmates to flee, including himself, as well as premeditated killing of officers, soldiers and prisoners".
Mr Morsi and several Muslim Brotherhood leaders were freed during a breakout at a Cairo prison in January 2011.
Our correspondent says the order provides legal cover for the continued detention at a time when the UN and Western powers are calling for Mr Morsi to be released or properly charged.
Muslim Brotherhood spokesman Gehad el-Haddad described the accusations as "ridiculous". He told Reuters news agency that the order marked the return of the "old regime".
Hamas itself said there was not a shred of evidence of its involvement in the prison break.
Mr Morsi narrowly won the presidential election in June 2012 but his opponents accused him of trying to impose an Islamist agenda on the country.