Security forces have cleared a Cairo mosque after a gun battle with followers of the Muslim Brotherhood, while Egypt's army-backed government, facing deepening chaos, considered banning the Islamist group.

Reuters witnesses saw gunmen shoot from a window of the al-Fath mosque, where supporters of deposed president Mohamed Mursi had taken shelter during ferocious confrontations in the heart of the Egyptian capital on Friday.

Another gunman was shown on television shooting from the mosque's minaret and soldiers outside returning fire.

Hours later, police moved in and secured the building, making scores of arrests.

It was not clear if anyone died in the clashes - the fourth day of violence which has killed more than 700 people.

Trouble was also reported in the second city Alexandria. An office run by the Muslim Brotherhood was set ablaze and a security source said a pro-Mursi protester was killed.

With anger rising on all sides, Prime Minister Hazem el-Beblawi proposed disbanding the Brotherhood, raising the stakes in a bloody struggle between the state and Islamists for control of the Arab world's most populous nation.

"We are not facing political divisions, we are facing a war being waged by extremists developing daily into terrorism," presidential political adviser Mostafa Hegazy told reporters.

"We will win this war not only with security procedures, but according to the law and within the framework of human rights."

If Mr Beblawi's proposal to disband the Brotherhood is acted on, it would force the group underground and could herald large-scale arrests of its members, placed outside the law.

Many Western allies have denounced the recent wave of killings, including the United States, alarmed by the mayhem in a country which has a strategic peace treaty with Israel and operates the Suez Canal, a major artery of global trade.

However, Saudi Arabia threw its weight behind the army-backed government on Friday, accusing its old foes in the Muslim Brotherhood of trying to destabilise Egypt.

The health ministry said 173 people died in clashes across Egypt on Friday, including 95 in central Cairo, after the Brotherhood called a "Day of Rage" to denounce a crackdown on its followers on Wednesday that killed at least 578 people.

Among those killed was a son of Muslim Brotherhood leader Mohamed Badie, shot dead near the al-Fath mosque.

Fifty-seven policemen have also died over the past three days, the interior ministry said.

The authorities said they arrested more than 1,000 people after Friday's protests, and one handcuffed man was shown on television with a gun on his lap. The state news agency said 250 Brotherhood followers faced possible charges of murder, attempted murder and terrorism.

Security sources said Mohamed Al-Zawahiri, the brother of al Qaeda leader Ayman Al-Zawahiri, had also been detained.

"Friday was a very bad, ugly day. There were attacks on police stations, ministries. The situation is very bad," the prime minister told reporters. "There will be no reconciliation with those whose hands have been stained with blood and who turned weapons against the state and its institutions."