Cairo: At least 16 people have died and dozens more were wounded after police attacked crowds of protesters calling for the reinstatement of Mohamed Mursi as president.

A field hospital at the Rabaa Al-Adawiya Mosque in Nasr City says it has been overwhelmed with injured protesters after police began firing tear gas into the crowds, leading to fierce clashes between demonstrators and security forces. Doctors say they are treating gunshot wounds and other injuries.

There are conflicting reports on the numbers killed, with the Muslim Brotherhood reporting that at least 38 people have died.

"They are not shooting to wound, they are shooting to kill," Brotherhood spokesman Gehad el-Haddad told Reuters.

It was the second time this month there had been a mass killing of pro-Mursi supporters. On July 8, 53 people died when armed men shot into a crowd after morning prayers at a vigil outside the Republican Guard compound near Nassr City.

Like that attack, the shooting around Rabaa Mosque began soon after 3am prayers, starting on the fringes of the vigil and continuing for hours after the initial push back against protesters by police.

Mr Haddad says at least 70 people died in the clashes and warned the toll could climb even higher. Associated Press is reporting 38 dead, but as many of the casualties were taken to nearby hospitals outside the area it remains difficult to get an accurate toll of dead and wounded.

It was a move that the pro-Muslim Brotherhood demonstrators had been fearing following a huge turnout of Egyptians on Friday night to support the country's military leader and defence minister General Abdel Fattah al-Sisi, who called on people to come onto the streets to give him a mandate to fight "terrorism".

Commentators said it was widely understood that General al-Sisi was talking about the weeks of pro-Muslim Brotherhood protests that had paralysed parts of Nasr City and Giza since the latest political crisis gripped Egypt just prior to the downfall of Dr Mursi on July 3.

Early on Saturday the Interior Minister in the interim, military-backed Egyptian Government, Mohammed Ibrahim vowed to end the sit-in at the mosque.

At least seven people were killed in Egypt's second city of Alexandria after clashes between supporters and opponents of Dr Mursi, while 274 were injured around the country in Cairo, and the governorates of Damietta, Gharbiya, Sharqiya and the Nile Delta, Egypt's ambulance authority reported.

Crowds had continued to march towards Tahrir Square late into the night, packing onto Qasr al-Nil Bridge and well back along the gridlocked roads leading to the iconic heart of Cairo's Downtown — the birthplace of Egypt's January 25 revolution that overthrew former dictator Hosni Mubarak.

The mood was celebratory. Fireworks exploded throughout the capital and carloads of jubilant demonstrators with Egyptian flags fluttering from the windows jammed the roads, beeping their horns.

There were also pro-military protests outside the Presidential Palace and in towns and cities throughout Egypt.

For those celebrating the end of the Muslim Brotherhood's rule, it was difficult to hide their delight.

Ahmad Omari works in a cotton factory in the outer-Cairo suburb of Haram, and over the year of Dr Mursi's rule he watched his livelihood disappear with every passing day.

He is paid on a piece-by-piece basis and economic conditions became so bad that his boss was unable to continue paying him. The business, like so many around Egypt, has yet to recover, he said.

"I am here to support General al-Sisi because I believe he will help Egypt to become stable again," Mr Omari said in Tahrir Square.

"The Ikwan [Muslim Brotherhood] stole Egypt from us once, they should not be allowed to take it again"

Across town in rival demonstrations, tens of thousands gathered to protest against the military and their decision to force Dr Mursi from the presidency on July 3 in what they describe as a coup.

There were also pro-Mursi demonstrations near Cairo University in Giza and elsewhere around the country.

"Sisi is a serial killer," a Muslim Brotherhood supporter yelled at Egyptian soldiers guarding a government building near the entrance to Rabaa. "We are not terrorists," another protester said. "We support democracy, and our democracy and our president have been taken away."

The demonstrations came as a judge announced Dr Mursi had been formally detained for another 15 days over accusations he conspired with the militant Palestinian group Hamas in attacks that killed policeman during Egypt's 2011 revolution, as well as claims he helped organise prison breaks.

Senior Muslim Brotherhood officials dismissed the claims as "ridiculous".

In Gaza, Hamas spokesman Sami Abu Zuhri condemned the extension of Dr Mursi's detention as well as the attempt to "drag Hamas into the Egyptian conflict".