Egyptian police exchanged gunfire Saturday with Islamist supporters of ousted president Mohamed Morsi holed up inside a Cairo mosque, an AFP correspondent reported.

The clashes came on the fourth day of bloodshed between the two sides, with the government saying 173 had died in the past 24 hours alone.

That brought the country's toll to more than 750 people since Wednesday, when 578 people were killed in nationwide clashes that erupted after police cleared two camps of Morsi loyalists in the capital.

The standoff at Cairo's Al-Fath mosque in central Ramses Square began on Friday, with security forces surrounding the building where Islamists were sheltering and trying to convince them to leave.

The Islamists had lined up the bodies of dozens of protesters killed in "Friday of anger" demonstrations inside the mosque-turned-morgue.

One of the protesters told AFP by telephone that they were demanding they not be arrested, or attacked by hostile civilians outside.

By Saturday afternoon, the situation turned violent, with an AFP reporter on the scene saying gunmen inside the mosque were trading fire with police outside.

The correspondent said police stormed the Fath mosque and security forces firing tear gas.

In the process, they managed to drag outside seven or eight men and were then confronted by angry neighbourhood residents who attacked them with sticks and iron bars.

Police fired in the air in a bid to disperse the mob.

An AFP reporter saw one man dressed in civilian clothes was wounded by police gunfire.

The violence has left Egypt divided as never before in recent history, splintering the army-installed interim government and inviting international censure.

Both outside the mosque and in several other parts of Cairo, residents targeted those suspected of being Islamists, often for no more than wearing a beard or a veil.

On Friday, Morsi supporters had announced "Friday of anger" demonstrations, which quickly turned violent, with gunshots ringing out in several parts of Cairo.

The government said those clashes killed least 173 people across the country, including 95 in Cairo and 25 in Alexandria.

Among those killed on Friday was the son of Mohamed Badie, chief of Morsi's Muslim Brotherhood.

The Anti-Coup Alliance of Morsi supporters announced it would end the protests shortly after a night-time curfew came into effect, but pledged daily demonstrations going forward.

The interior ministry said it had arrested 1,004 Muslim Brotherhood "elements", and on Saturday security sources said the brother of Al-Qaeda chief Ayman al-Zawahiri had been detained.

And security sources said authorities had arrested the brother of Al-Qaeda chief Ayman al-Zawahiri, a Morsi supporter.

The Egyptian cabinet issued a defiant statement on Friday night saying it was confronting a "terrorist plot."

"The cabinet affirms that the government, the armed forces, the police and the great people of Egypt are united in confronting the malicious terrorist plot by the Muslim Brotherhood," it said.

And the interior ministry, which authorised police to use live fire if government buildings came under attack, said several attempts to storm buildings had been foiled.

Meanwhile, international criticism continued to pour in, with European leaders pledging a strong response and EU foreign policy chief Catherine Ashton describing the violence as "shocking."

"I have asked member state representatives to debate and coordinate appropriate measures to be taken by the European Union in response to the situation in Egypt," she said.

Germany said it would review ties with Cairo, and joined France and Britain in calling for EU talks on the situation, which are expected to take place on Monday.

Pope Francis said he was following events with "mounting concern" and was praying for the rival sides to "choose the path of dialogue and reconciliation," the Vatican press office said.

The United States has announced the cancellation of its biannual military exercise with Egypt, but stopped short of suspending $1.3 billion in annual aid.

Human rights organisation Amnesty International called for a full and impartial investigation into the bloodshed, saying the authorities' response to the protests had been "grossly disproportionate".

But the international response was not uniformly critical. Saudi Arabia and Jordan said they backed Egypt's fight against "terrorism".