After an overnight crisis meeting, the Egyptian government demanded an official apology and told Foreign Minister Mohamed Kamel Amr to summon the Israeli ambassador to protest.
Cairo is demanding a “joint official probe” as well as setting up its own inquiry into the deaths.
The Israeli military has promised to investigate the incident.
Angry crowds demonstrated outside Israel’s embassy in Cairo on Friday night, calling for the ambassador to be thrown out.
“What was tolerated in pre-revolution Egypt will not be in post-revolution Egypt,” Prime Minister Essam Sharaf declared on his Facebook page, distancing his government from the policy of rapprochement with Israel under former presidents Hosni Mubarak and Anwar Sadat.
Five Egyptian police officers were killed on Thursday "inside Egyptian territory as a result of an exchange of fire between Israeli forces and armed elements inside Israeli territory”, according to Information Minister Osama Heykal.
Another police officer was killed and a colleague seriously wounded in a border gunfight on Friday.
The Egyptian military has been conducting a week-long operation against armed Islamists in the Sinai peninsula after attacks on police and a pipeline to Israel.
The deaths came as Israel retaliated to Thursday’s rocket attacks on its territory. The state-owned Al Ahram newspaper quoted a military official saying that the men were shot by gunmen trying to slip across the border from Israel.
The Israeli air force continued air raids on the Gaza Strip overnight, claiming to have targeted “terror tunnels”, an arms dump and a “terror activity site”. Palestinians reported no casualties but said raids on Friday killed 14 people and wounded over 40.
As many as 12 rockets were fired from Gaza into Israeli territory, with the only casualties being three Palestinians, who were sleeping rough. They had entered Israel illegally to find work, according to police.
The Popular Resistance Committees, a radical group that Israel blames by for killing eight Israelis on Thursday, claimed responsibility. Islamic Jihad and the left-wing Popular Front for the Liberation of Palestine also issued statements saying they took part.