The security cabinet on Thursday approved a request from Defense Minister Ehud Barak to allow Egypt to deploy attack helicopters in Sinai.
The approval was necessary because under the Camp David accords there are strict limits on the type of weaponry that can be brought into the area.
The approval came a day after the Egyptian army used air power against terrorists in the region.
The state of lawlessness which Egypt is attempting to bring under control in the peninsula was underscored Thursday when gunman fired shots towards a police station in the main administrative center of North Sinai.
Hundreds of troops in armored cars drove out of the town to hunt Islamist terrorists blamed for killing 16 Egyptian border guards on Sunday, the biggest spike in violence which has been growing steadily since last year's overthrow of Hosni Mubarak.
The gunfire in al-Arish, the nerve center of the government's otherwise shaky control of the North Sinai region, showed how difficult it will be for Egypt to impose order. It followed attacks on checkpoints in the town on Wednesday.
Israel has welcomed Egypt's offensive while continuing to express worries about the deteriorating situation in Sinai, home to anti-Israel terrorists, Beduin tribes angered by neglect by Cairo, gun-runners, drug smugglers and al-Qaida sympathizers.
Barak said Egypt was acting "to an extent and with a determination that I cannot previously recall".
"Whether this ends with (their) regained control of Sinai and allows us not to worry as much as we have in the past few months, this I do not know," he told Israel Radio.
The unidentified gunmen in al-Arish fled before police could respond, a security source said, denying a report by state television that police had fought back.
Hundreds of troops and dozens of military vehicles had reached the town, security sources said, part of an offensive not seen since Egypt's 1973 war with Israel.
Dozens of armored vehicles, some equipped with machine-guns, could then be seen driving out of al-Arish towards the settlement of Sheikh Zuwaid which military aircraft attacked on Wednesday. The troops saluted passers-by and flashed victory signs, or filmed their departure with video cameras.
Egypt's President Mohamed Morsy - whose Islamist background in the Muslim Brotherhood has been eyed with suspicion by Israel since he was elected in June - on Wednesday fired the region's governor and country's intelligence chief in response to public anger over Sunday's attack.
No one has claimed responsibility for the assault, in which the assailants seized two armored vehicles to storm an Israeli border crossing. One made it through before the attackers were killed by Israeli fire.
Israel says terrorists based in Sinai and Palestinian hardliners in neighboring Gaza pose a growing threat to its border. It says Palestinians use illegal tunnels to smuggle in guns and travel across to join those on the Egyptian side.
Israel has also been wary of Morsy's ideological affinity with Hamas, the Islamist group ruling Gaza, fearing he would take a softer position on Palestinian militancy than Mubarak.
Morsy has brushed aside accusations that his politics would make it difficult for him to take a strong stance against violent groups sworn to Israel's destruction.