Hundreds of supporters of deposed Egyptian President Mohamed Morsi remain trapped in a mosque near Cairo's Ramses Square after security forces escorted several of them out.

The standoff at the Egyptian capital's Fateh Mosque, which began late on Friday night, stretched into Saturday morning amid reports of offers of safe passage.

Speaking to Al Jazeera by phone from inside the mosque, Omaima Halawa said there were about 700 people, including women and children, inside and that they feared leaving the mosque because "there were thugs outside with the security forces, and that ... the security forces were working with the thugs".

She said she feared about what might happen to her or where she would be taken if she left the mosque.

Egypt's Nile News reported that about 10 people, mostly women, left the mosque accompanying the body of a woman who had died on Friday.

Al Jazeera Mubasher Misr said the protesters had been offered safe passage out of the mosque on the condition they would be subjected to investigation in an army camp.

The protesters rejected the conditions and insisted that any investigation be conducted inside the mosque, the TV station said.

For his part, the Egyptian army's spokesman said via Facebook that armed men had been shooting from the mosque at nearby buildings.

Violence erupted across Egypt again on Friday after the Muslim Brotherhood and other groups, under the banner of the Anti-Coup Alliance, called for protests in defiance of a security crackdown on pro-Morsi sit-ins that had left more than 600 dead since Wednesday.

At least 173 people were killed and 1,330 others were injured nationwide as protesters tried to stage Day of Rage marches against the military-led government, according to a government spokesman.

Police also arrested more than 1,000 suspected Muslim Brotherhood supporters, including 558 in Cairo alone, on Friday, the Interior Ministry said in a statement.

The Fateh Mosque had been turned into both a morgue and a field hospital by Morsi supporters until the standoff with security forces began.

In another development, Morsi'sFreedom and Justice Party (FJP) confirmed on Saturday that Ammar al-Badie, son of the Muslim Brotherhood's supreme guide, Mohamed al-Badie, was among those killed in Ramses Square in Friday's violence.

He was shot twice in the head and eyes, FJP said.

Badie is the third child of a high-ranking Brotherhood member to be killed this week. The other two died on Wednesday: Hafsa al-Shater, the daughter of the group's top strategist, Khairat al-Shater; and Asmaa el-Beltagy, the daughter of Mohamed el-Beltagy, the FJP head.

Live fire use authorised

The Muslim Brotherhood has called for a week of fresh demonstrations across Egypt following the latest deaths.

An interim cabinet, installed by the army after it removed Morsi during rallies against his rule, has refused to back down in the face of the ongoing protests.

It has authorised police to use live ammunition to defend themselves and state installations.

Bader Abdel Atty, a spokesman for the Egyptian Foreign Ministry, defended the actions of the security forces in an interview with Al Jazeera on Friday, saying that protesters were armed with machine guns.

"They are raising al-Qaeda flags in the heart of Cairo," he said.

"They are using machine guns against civilians. And this cannot be described as far as I know as a peaceful demonstration," he said.

Abdel Atty dismissed international condemnation of the violence and said Egypt would accept no external interference.

Many Western allies have condemned the killings, including the US, but Saudi Arabia threw its weight behind the Egyptian government on Friday, accusing the Muslim Brotherhood of trying to destabilise country.

However, with no compromise in sight, the most populous Arab nation - which is often seen as leading events in the entire region - looks increasingly polarised and angry.

A number of tour operators have suspended all holidays to Egypt until at least next month and the US has urged its citizens to leave the country.

The EU has asked its states to consider "appropriate measures" to take in reaction to the violence, while Germany said it was reconsidering its ties.