Egyptian President Muhammad Mursi has vowed he would retake “full control” of the Sinai after unidentified gunmen attacked a checkpoint on the Egyptian-Israeli border on August 5, killing 16 guards.
Israel said the attackers, in two vehicles, then tried to enter Israeli territory.
One vehicle apparently blew up at the crossing, while the other was destroyed in an Israeli air strike.
Israeli Prime Minister Benjamin Netanyahu hailed "the determined action of the military" and domestic intelligence agency Shin Bet "for ensuring the failure of a large attack on Israeli civilians."
After an emergency meeting with Egyptian military and security officials, President Mursi told state television that orders had been given to our armed forces and police to chase and arrest those who carried out this assault.
A top Egyptian security official was quoted as saying the gunmen were "jihadists" who had infiltrated from the Gaza Strip.
State media said Egypt was closing its Rafah frontier crossing with the Hamas-controlled Gaza Strip "until further notice."
The attack is an early test for Mursi, who took office in June after Hosni Mubarak was overthrown in a popular uprising last year.
It could also complicate Cairo’s relations with the Hamas militant group, which is close to Mursi's Muslim Brotherhood.