Israeli warplanes launched air strikes on Gaza and militants fired more than 10 rockets into Israel, the Israeli authorities said early Friday, a day after armed attackers, described by the authorities as Gazans who had crossed into Israel from Egypt, carried out multiple deadly attacks near the popular Red Sea resort of Eilat.

Tensions threatened to escalate further Friday after Egyptian security officials said Israeli forces attacking suspected terrorists in the border area inadvertently killed two officers of the Egyptian security police and a third officer in the Egyptian Army, all on the Egyptian side of the border.

Egyptian officials said that an Israeli aircraft had fired at people suspected of being militants who were fleeing across the border into a crowd of Egyptian security personnel and that the three Egyptians were killed.

The accidental killings were almost certain to inflame animosities toward Israel among the Egyptian public. Long suppressed under the deposed President Hosni Mubarak, such feelings have increasingly poured out into street protests and the news media since the Egyptian revolution.

Israel seemed anxious to play down the reported killings, with the military saying its forces had nothing to do with any incident Friday along its border with Egypt, while Mark Regev, a government spokesman, suggested that the reports of Egyptian fatalities may have been related to clashes between Egyptian security forces and militants. An Egyptian government spokesman referred to Egyptian news media reports of the killings and said government officials were still assessing the situation.

By Friday morning, Gaza militants had fired more than 10 rockets at southern Israeli cities, according to the Israeli military. One fell near a religious seminary in Ashdod, apparently causing some injuries.

In response to both the rocket attacks and the assaults on Thursday near Eilat, the Israeli military said in a statement early Friday that its warplanes struck seven targets in the Gaza Strip overnight.

“In northern Gaza, the targets included a weapon manufacturing site and two terror activity sites. In southern Gaza, the targets included two smuggling tunnels, a terror tunnel and a terror activity site,” the statement said, without elaborating further on the nature of the targets.

Eight Israelis were killed and more than 30 were wounded on Thursday in the attacks near Eilat, the most serious on Israel from Egyptian territory in decades. The attacks highlighted how the fallout from the Egyptian revolution — lawlessness in the northern Sinai Peninsula and a softer line in Cairo toward Iran and the militant group Hamas — had frayed ties with Israel.

The Israeli military said it had killed at least four of the attackers in the desert near the Egyptian border. Hours later, it retaliated with several airstrikes on Gaza. In the first such strike, six Palestinians, several of them members of a militant group, were killed, according to the group’s spokesman and medical officials in Gaza.

The attacks near Eilat were the deadliest in Israel since Prime Minister Benjamin Netanyahu took office two and a half years ago, and they come at a time of great uncertainty as the Palestinians plan to seek recognition of statehood at the United Nations in the fall.

The defense minister, Ehud Barak, described the attacks as “a grave terrorist incident” that had originated in Gaza and could probably be attributed to the “loosening” of Egypt’s hold over Sinai since the revolution. Yet Israel appeared reluctant to blame the Egyptian authorities, not wanting to inflame an already delicate situation and preferring to use the events to urge more constructive Egyptian action.

“Our hope,” one Israeli official said, “is that this tragedy will serve as an impetus for the Egyptians to firmly exercise their sovereignty in all of Sinai and to end the security vacuum that has started to emerge there.”

In a short, televised address to the nation on Thursday night, Mr. Netanyahu did not mention Egypt by name and directed the blame at Gaza, which is governed by Hamas. Referring obliquely to that evening’s first swift airstrike on Gaza, he said, “Those who gave the order to murder our citizens, while hiding in Gaza, are no longer among the living.”