The air strikes around the town of Sheikh Zuwaid, six miles from the Palestinian-ruled Gaza Strip, followed clashes between armed men and Egyptian security forces in the Sinai region.
Gunmen killed 16 border guards at a checkpoint on Sunday. The attackers stormed through the border into Israel but they were killed by Israeli fire.
The militants, who are sworn to destroy Israel, have stepped up their actions along the isolated desert frontier since an uprising toppled Egypt's autocratic leader Hosni Mubarak last year. The new president, Mohamed Mursi, a moderate Islamist who took office in June, has tried to allay Israeli concerns with promises to bring the region back under government control.
The Egyptian army, which kept peace with Israel throughout the Mubarak years, still keeps broad sway over national security. But Mr Mursi has also brought Egypt closer to the Islamist Hamas movement, making this a delicate time in relations between the Jewish state and the Arab power.
Israel said Egypt's action against the militants was a necessary response against groups threatening its security.
Egyptian army rockets have not been fired in the area since the 1973 war with Israel and the military operation appeared to be the biggest there since the peace treaty was signed.
The militant strongholds are in northern Sinai, away from the Red Sea resorts further south that are popular with foreign tourists and a lifeline for Egypt's struggling economy.
Witnesses in Sheikh Zuwaid said they saw two military planes fly over the area and heard explosions yesterday. Other people near the town said they saw three cars bombed.
Troops entered the village of al Toumah, 15 miles further south, after the army received information Islamist militants were staying there.
A military commander said his troops had killed 20 militants and destroyed three armoured cars belonging to terrorists.
A villager said he saw heli-copters chasing the vehicles out of al Toumah and heard rocket fire. The men in the cars shot back with machine guns, he said.
The crackdown came after armed men opened fire on several checkpoints in al Arish – the administrative centre for northern Sinai – on Tuesday.
Gunmen also attacked checkpoints in Rafah, Egypt's entry point into the Gaza Strip that borders both Israel and Egypt.
The military response focused immediately on Sheikh Zuwaid, an economically deprived town that has come to rely heavily on profits from smuggling goods and people through tunnels into Gaza since the Palestinian territory was cut off from Israel.
The government in Cairo said the gunmen behind Sunday's attack had reached Egypt via the tunnels and it has begun work to seal them off.
Israel has long accused Palestinian jihadi groups of crossing from Gaza to Egypt to team up with local militants with the aim of attacking Israel's long border. Eight Israelis have been killed in border attacks in the past year.
Hamas condemned Sunday's attack and said it was trying to help Egypt identify the gunmen.
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