Egyptian authorities said Saturday that Israel’s statement of regret for the killing of three Egyptian security officers was inadequate, according to the state news agency MENA. But they retreated from their earlier threat to recall their country’s ambassador to Israel.

“The Israeli statement was positive on the surface, but it was not in keeping with the magnitude of the incident and the state of Egyptian anger toward Israeli actions,” a Cabinet statement said, according to MENA. Authorities also demanded a timetable for Israel’s offer of a joint investigation of Thursday’s killings.

Earlier in the day, Egypt had threatened briefly to recall its ambassador, prompting an expression of regret from the Israeli defense minister, two days after at least three Egyptian security personnel were killed by gunfire at the border after a deadly attack in southern Israel.

The border killings, which have been blamed in Egypt on an Israeli helicopter tracking the attackers, have sparked a public outcry here and prompted calls by political parties and civic organizations for Egypt’s interim military leadership to respond and to reassess the 1979 peace treaty with Israel.

On Saturday and into Sunday morning, thousands of people gathered outside the Israeli Embassy to protest the killings. At one point, the Israeli flag was removed from the building and replaced with an Egyptian flag.

In an effort to head off a diplomatic crisis, Israeli Defense Minister Ehud Barak issued a statement Saturday expressing regret over the deaths of an Egyptian soldier and two police officers at the border, promising a joint investigation of the incident and commending Egypt’s conduct in the relationship with Israel.

“Israel regrets the death of the Egyptian policemen during the attack on the Israeli-Egyptian border,” the statement said. Barak did not acknowledge Israeli responsibility for the deaths.

The ruling military council faces a dilemma, observers said. If its response is seen as too weak, it risks fueling public resentment. If its statement is too strong, it could jeopardize Egypt’s relationship with Israel and anger its ally the United States.

“As far as the Egyptian ruling power is concerned, I don’t think they want to see any tension,” said Hani Shukrallah, editor in chief of the English-language al-Ahram Online Web site. The Israelis, he said, “are putting the Egyptian authorities in a very embarrassing situation before their public at a time when it’s very difficult not to be responsive to public opinion in post-revolution Egypt.”

The Egyptian government had demanded an Israeli apology and joint probe, and it criticized statements by Israeli officials about Egypt after the raid that left eight Israelis dead. Barak said at the time that Egypt’s hold on the Sinai Peninsula, from where the attackers are thought to have infiltrated Israel, had weakened.

In the statement Saturday, Barak said that he had ordered a military investigation of the incident, followed by a joint inquiry with the Egyptian army.

“Defense Minister Barak noted the importance of the peace treaty with Egypt and our appreciation for the judgement and responsibility shown by Egypt,” the statement said.

Earlier, Amos Gilad, a senior Israeli Defense Ministry official, said it was unclear whether the Egyptian fatalities had been caused by Israeli fire or the gunmen who were being pursued.

“No one in Israel wants to harm Egyptian soldiers and policemen,” Gilad told Israel Radio. “No soldier consciously aims at Egyptian soldiers and police.”

“The army returned fire to sources of shooting and murderers who wanted to kill civilians,” Gilad added. “It all has to be checked thoroughly and professionally.”

Egyptian officials later stepped back from the decision to withdraw their ambassador to Israel, saying it was under review.

Meanwhile, a flare-up of violence triggered by Thursday’s attacks continued Saturday. Israeli aircraft struck targets in the Gaza Strip, and militants in the coastal territory fired fresh volleys of rockets and mortars at southern Israel. The Israeli military said its airstrikes targeted a mortar squad, a weapons storage facility, tunnels and a militant training site. Two people were reported wounded, one seriously.

One Israeli was killed and four seriously wounded in the city of Beersheba, where a rocket struck a house and a car, emergency services said.

The armed wing of the Islamist group Hamas, which rules the Gaza Strip, joined the firing for the first time, targeting the town of Ofakim, where a house took a direct hit and three people were slightly wounded, according to reports from the scene.

An early-morning attack on the coastal city of Ashdod wounded three Palestinian laborers who had entered Israel without permits and were sleeping in a grove. Two were reported in serious condition.

Fourteen Palestinians have been killed in the Israeli strikes since Thursday, most of them militants, but also several civilians, including two children. More than 40 have been wounded, medical officials said.

The United Nations, the United States, the European Union and Russia issued a statement Saturday condemning Thursday’s attacks in Israel “in the strongest terms” and calling on the Egyptian government to “find a lasting resolution to the issue of Sinai security.”

In Egypt, political parties across the ideological spectrum issued condemnations of Israel on Saturday. Almost all called for reassessment of the 1979 peace treaty with Israel, which limits the number of security forces and the kinds of weapons allowed in the Sinai Peninsula. Political groups also called for full sovereignty in the Sinai, the immediate expulsion of the Israeli ambassador, the recall of Egypt’s ambassador and a halt to the export of natural gas to Israel.

“The peace agreement is a contract between two sides, and Israel has not respected the conditions of this agreement,” said El-Sayyed el-Badawi, head of the liberal al-Wafd party. “If they do not respect it, then it should be canceled.”

Greenberg reported from Jerusalem. Special correspondents Islam Abdel Kareem in Gaza and Muhammed Mansour in Cairo contributed to this report.