The Monday firefight with bedouin men erupted in the mountainous interior of the Sinai peninsula about 30km from the scene of Saturday's attacks on the coast, security officials said.
It came after police surrounded the nearby villages of Khurum and Rweissat in overnight raids, they said.
"Two Pakistanis had been staying there, and it is suspected that the bombs were assembled in this area," an intelligence source said.
Pictures of the six Pakistanis believed to have entered Egypt in early July were distributed to police stations in the Sharm al-Shaikh area after the attacks, which followed other bombings in Sinai resorts in October.
Their passports were found in an unspecified Sharm al-Shaikh hotel, police said, adding that one of them might have died in the deadly bombings, but stressing that the Pakistanis were not necessarily the bombers.
Pakistani authorities said they had yet to be approached by their Egyptian counterparts about the six suspects.
Pictures of more than 30 other suspects were also distributed, mostly Egyptians, as well as internationally wanted "terror" suspects.
Pictures of suspects have been
distributed by the police
At least 130 people have been arrested in a police dragnet as part of a search for the perpetrators of the attack on a hotel, a market and a parking lot that came after deadly bombings in London.
On Monday, the government also sacked the heads of security in North and South Sinai provinces - a sign of security failures that may have allowed the assault on one of Egypt's most closely guarded towns.
Hospital officials say the three bombings - Egypt's deadliest attacks - killed 88 people, while the health and tourism ministries have confirmed 64 dead.