At least 54 people have been reported dead in clashes with anti-government protesters in Egypt on the third anniversary of the uprising that culminated in the overthrow of Hosni Mubarak as president.

Thousands of Egyptians also rallied in support of the army-led authorities, underlining the country's deep political divisions.

The majority of the deaths were in Cairo, according to the health ministry. Security forces lobbed teargas and fired in the air to try to prevent anti-government demonstrators from reaching Tahrir Square, the symbolic heart of the 2011 uprising, where government supporters called for the head of the military, General Abdel Fattah al-Sisi, to run for the presidency.

Armoured personnel carriers were deployed to try to keep order and anyone entering Tahrir had to pass through a metal detector.

Elsewhere in Cairo, supporters of the man Sisi toppled last July, the Muslim Brotherhood's Mohamed Morsi, marched in over 30 neighbourhoods to protest against Morsi's overthrow. There were smaller gatherings of pro-democracy activists who are opposed to the authoritarianism of both men.

The protesters defied threats of violence from an al-Qaida-inspired group, Ansar Beit al-Maqdis, which claimed responsibility for a series of bomb blasts in Cairo on Friday that targeted police and killed at least eight people.

In the southern town of Minya, two people were killed in clashes between Morsi supporters and security forces, said Brigadier General Hisham Nasr, the director of criminal investigations in the regional police department.

A woman was killed in Egypt's second city, Alexandria, during clashes between supporters of Morsi and security forces.

The scene inside Tahrir was a stark contrast to that three years ago when anti-government protesters clashed with police. Those in control of the square on Saturday were supporters of the police and Egypt's security establishment, with several men seen kissing policemen and soldiers as they entered the square.

"The police are our brothers, our people, our sons," said Khaled Nasredeen, a 45-year-old trader, who carried a banner calling for Sisi to run for the presidency. "The problems between the people and the police – it was a trick played on us by the Muslim Brotherhood."

Other pro-government demonstrators said a security state, led by a military strongman such as Sisi, was the only solution to the political and economic chaos since the 2011 uprising.

"We pray for stability. We've never seen such a bad situation in Egypt, not even during the 1973 war," said Atef Hayal, who travelled hundreds of miles to attend the rally. "Sisi is the only guy who can protect Egypt."

A few miles west, at Mostafa Mahmoud square, pro-democracy activists expressing the opposite viewpoint were prevented from gathering for a march by police. "As soon as I got to Mostafa Mahmoud, two cops came up to me, kept kicking me and telling me to get the fuck out or else they'll jail me," tweeted a leftwing activist, Tarek Shalaby.

Police later attacked another leftist rally near Tahrir Square, continuing a crackdown on all forms of dissent that has seen thousands of Islamists and dozens of secular activists arrested since July.

"This is not the Egypt that we are looking for," said a spokesman for the 6 April group, the youth movement that organised many of the first protests against Mubarak in 2011.