The Muslim Brotherhood said at least 31 people were killed on Saturday when security forces opened fire on a protest by supporters of deposed president Mohamed Morsi in Cairo.

"They are not shooting to wound, they are shooting to kill," Muslim Brotherhood spokesman Gehad El-Haddad said. "The bullet wounds are in the head and chest."

The violence erupted on the fringes of a round-the-clock vigil staged by backers of Morsi, who was ousted from power earlier this month by Egypt's military following mass protests against his first year in office.

Al Jazeera's Egypt television station showed medics desperately trying to revive casualties arriving at a field hospital at the Brotherhood sit-in at Rabaa al-Adawiya, a mosque in north-east Cairo.

A doctor at the field hospital said at least 16 people had died.

Yehia Mikkia said the overnight clashes had overwhelmed the hospital operating from the sit-in, where the protesters have been camped for more than three weeks.

Police fired tear gas to disperse hundreds of Morsi supporters near the sit-in, setting off clashes that lasted for hours.

El-Haddad said police started firing repeated rounds of tear-gas at protesters on a road close to the mosque sometime after 3am local time (2am BST). Shortly afterwards, live rounds started flying, hitting people at close range.

The bloodshed came the day after supporters and opponents of Morsi staged mass rival rallies across the country, bringing hundreds of thousands into the streets and laying bare deep divisions within the Arab world's most populous country.

Well over 200 people have died in violence since the overthrow of Morsi, most of them Brotherhood supporters.

There was no immediate word from the security forces about what they thought had happened at Rabaa early on Saturday.