Thousands turned out for rival protests in Cairo on Friday, exposing the widening rifts among Egyptians over the ruling military's handling of transition from Hosni Mubarak's rule.

Crowds gathered in Tahrir Square to denounce the Supreme Council of the Armed Forces (SCAF), expressing their fury over footage of soldiers beating female protesters during deadly clashes that sparked international outrage.

Thousands more anti-military protesters turned out in the Mediterranean city of Alexandria and the canal city of Suez to demand the ruling generals, who took power when a popular uprising ousted Mubarak in February, immediately hand power to civilian rule.

Nearly two months of clashes between protesters and soldiers have left more than 60 people dead and overshadowed the first parliamentary elections since Mubarak's downfall.

The violence, particularly the beating of women, has piled pressure on the SCAF, as liberals and Islamists facing off in the polls condemned the military's handling of protests.

"Women are a red line!" some protesters shouted in Tahrir Square as others chanted against Field Marshal Hussein Tantawi, the head of the ruling SCAF and Mubarak's longtime defence minister.

Sheikh Hisham Attiya, the imam leading the Muslim noon prayers in the square, called for an independent panel to investigate the deaths and prosecute those responsible.

Protesters accusing the military of using Mubarak-era methods to stifle dissent have launched a campaign calling for presidential elections to be held on January 25, one year after the launch of protests that brought down the veteran strongman.

"The military council is an extension of the old regime; it has the same mentality and uses the same tactics," said protester Mohammed Farrag, 31.

The SCAF denies ordering the use of force against protesters but has apologised to the women of Egypt for "any transgressions" after several shocking videos have surfaced showing brutality against protesters.

"If they think beating women up is going to silence the protesters, they are wrong," said one woman, Mona Ahmed.

Videos posted on social networking sites over the past week show soldiers savagely beating women with truncheons or throwing them to the ground.

In one instance, which drew worldwide attention, a veiled woman was thrown down, her top ripped away to expose her bra and a soldier kicked her in the chest.

The beatings sparked a backlash, with thousands of women marching through Tahrir Square on Tuesday in protest against the military junta.

London-based watchdog Amnesty International called on the SCAF to uphold the right to peaceful demonstration.

"The shockingly violent scenes of recent days must not be repeated," said Philip Luther, Amnesty International's interim director for the Middle East and North Africa.

"Egypt's military authorities must ensure protesters are allowed to exercise their right to freedom of expression peacefully, without fear of attack. The authorities are responsible for the safety of those protesting," he said.

The UN women's agency on Thursday expressed "great concern" over the recent attacks on women, which US Secretary of State Hillary Clinton denounced as a "disgrace."

Meanwhile, thousands of pro-military demonstrators gathered in the Abbasiya neighbourhood, several kilometres from Tahrir Square, under large banners bearing the pictures of the ruling generals.

Waving Egyptian flags, they demanded "the downfall of Tahrir" and insisted "the people and the army are one."

"We are here to support stability," said Mamduh al-Sayyed. "The January 25 revolution was honourable, but things have gone too far. We have now entered a parliamentary phase."

"I'm here to save Egypt from what is happening in Tahrir," said Ahmed Fathi, echoing the view of many who feel that the anti-military protesters are standing in the way of the country's stability.

"Egypt is not Tahrir and those in Tahrir don't represent all of Egypt," he said.

The rallies come as counting is underway after run-offs for the second phase of a staggered election for the lower house of parliament.

The country's two largest Islamist parties have emerged as front-runners so far.

The Muslim Brotherhood, whose political arm is leading in the parliamentary polls, refused to back Friday's protests.

The generals have pledged action against those responsible in an unusually contrite statement.

But they also warned against joining protests they said were aimed at toppling the state, and refused to move forward presidential elections from mid-2012.