Hasm is a group that has claimed several attacks around Cairo targeting judges and policemen since last year.
The suspected fighters tried to flee after the exchange of fire there, the sources said, and continued to shoot at a second security unit called in for back-up from atop neighbouring buildings.
The fighters also used explosive devices in the attack, the sources said, adding that 16 officers died in the shoot-out and the number was expected to rise.
Two security sources said eight security personnel were injured in the clashes, while another source said that four of the injured were police officers and four others were suspected fighters.
A number of suspected fighters were also killed and security forces were continuing to comb the area, a statement by the interior ministry said.
The Associated Press news agency quoted an Egyptian security official as saying the exchange of gunfire occurred in al-Wahat al-Bahriya, a district in the Giza governorate, about 135km from Cairo.
He too said eight other security personnel were wounded in the attack.
A convoy of four 4x4 vehicles and one interior ministry vehicle was ambushed from higher ground by the fighters firing rocket-propelled grenades and detonating explosive devices, a senior source in the Giza Security Office said.
Egypt accuses Hasm of being a wing of the Muslim Brotherhood, a group it outlawed in 2013. The Muslim Brotherhood denies the charge.
No group immediately claimed involvement in Friday's attack.
State of emergency
Egypt has been under a state of emergency since bombings and suicide attacks targeting minority Coptic Christians killed scores earlier this year.
A violent anti-government campaign in the Sinai Peninsula has grown since the military overthrew democratically elected President Mohamed Morsi of the Muslim Brotherhood in mid-2013.
The armed group staging the campaign later pledged allegiance to the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group in 2014.
It is blamed for the killing of hundreds of soldiers and policemen and has started to target other areas, including Egypt's Christian Copts.
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