Egyptian security officials say military helicopters have fired missiles on suspected Islamist militants in Toumah village in the Sinai peninsula.
Up to 20 people are reported to have been killed.
The strikes came after security checkpoints were allegedly attacked by gunmen in the town of al-Arish, leaving a number of people injured.
On Sunday, 16 Egyptian border guards were killed in the area.
After that attack, Israeli forces said they killed at least seven gunmen who broke through into Israel.
Patrols have been stepped up in Northern Sinai, and Egypt’s Rafah border crossing to Gaza has been indefinitely closed as security forces hunt the remaining attackers.
This is the first time Egypt has fired missiles in Sinai since the 1973 war with Israel, when it attempted to recapture the Sinai peninsula, security officials told Associated Press.
A Sinai army commander told Reuters news agency the army had received information that there were many militants in Toumah village.
“We have succeeded in entering al-Toumah village, killed 20 terrorists and destroyed three armoured cars belonging to terrorists. Operations are still ongoing,” he told Reuters.
The attack came hours after three security checkpoints were attacked in al-Arish, near the Israeli border.
Six people – including one civilian – were reportedly wounded in those attacks.
The Egyptian military also carried out separate helicopter attacks around an area called Sheikh Zuwayed just east of al-Arish, security officials said.
Both Israeli and Egyptian officials blamed Sunday’s attack on Islamist militants – though Egypt’s Muslim Brotherhood accused the Israeli spy agency Mossad of being responsible, a claim Israel rejected as “nonsense”.
The rising violence in the area is a test of credibility for the government of President Mohammed Mursi, the BBC’s Kevin Connolly says.
Israel wants tighter security in the Sinai, but it does not want that to be achieved with a large increase in numbers of Egyptian troops near its border, our correspondent adds.
Egypt’s military sent extra tanks and troops into the Sinai last year, under terms that had to be agreed with Israel under the 1979 peace treaty between the two countries, which returned Sinai to Egyptian control.