Gunmen killed 16 Egyptian border guards Sunday at a checkpoint near the Gaza Strip and Israel, and then stole security vehicles and attempted to cross into Israel.
Egyptian state media said Islamist militants from Gaza and the Sinai peninsula carried out the attack as the guards were breaking their Ramadan fast.
The Israeli military said the militants drove two Egyptian security vehicles to the Israeli border. It said one vehicle exploded and the second crossed the border and was destroyed in an Israeli air strike.
Israeli officials said seven militants were killed, four on the Israeli side of the border and three on the Egyptian side.
Egyptian President Mohammed Morsi called the attack "cowardly." The Egyptian government said it was closing Egypt's Rafah border crossing with Gaza.
Israeli Prime Minister Benjamin Netanyahu said determined action by the Israeli military prevented a major attack on civilians. Defense Minister Ehud Barak said the incident shows a need for Egypt to take determined action to prevent he calls "terror in Sinai."
Gaza's ruling Hamas movement condemned the attack on the Egyptian border guards and sent condolences to the families of those killed and to Mr. Morsi, whose Muslim Brotherhood group shares ideological roots with Hamas.
Sinai has become increasingly lawless since the ouster of Egyptian President Hosni Mubarak last year. Militants in Sinai have targeted Egyptian security forces, blown up pipelines supplying gas to Israel and Jordan and killed Israelis in cross-border attacks.