Ten policemen were wounded in the fighting that began on Tuesday when security forces killed one suspect, said a police official.
About 5000 police have surrounded about 120 armed men in the mountains near the resort town of Ras Sudr, 150km southeast of Cairo, said the official. Police believe two fugitives connected to the 7 October Sinai resort bombings are with the armed men.
Thirty-four people died in the near-simultaneous bombings at three beach resorts in Taba and Ras Shitan, also in the Sinai Peninsula. The bombings came at a time when resorts along Egypt's border with Israel were packed with Israelis taking advantage of a Jewish holiday.
Police officer dead
One police officer died of his wounds in a Cairo hospital, said the official.
Another, shot five times in the chest, died at the main hospital in Ras Sudr, according to a hospital official there.
Five Egyptian suspects were arrested in the weeks after the attacks, which Egyptian officials have linked to public anger over the Israeli-Palestinian conflict.