The Egyptian and Israeli governments moved Sunday to ease tensions over fatal cross-border attacks, apparently seeking to stop the crisis from flaring up into a full-scale diplomatic rift.

An Israeli official confirmed that an Israeli military delegation arrived in Egypt on Sunday, quietly and unannounced, for behind-the-scenes talks with Egyptian officials, and a second Israeli official issued a public statement of regret for the deaths of Egyptian soldiers.

The dispute arose Thursday after Palestinian militants carried out an attack in southern Israel, near the Egyptian border, killing eight Israelis. Israeli security forces chasing the militants fired into Egypt, killing three Egyptian soldiers in what officials have said was an accident.

Israel has yet to officially accept responsibility for the killings but has promised to hold a joint inquiry with Egypt to determine the facts.

The killings prompted an outpouring of rage against Israel in Cairo and provided a thorny diplomatic test for Egypt’s new military government, which has sought to maintain its peaceful relationship with Israel while being responsive to the street, where antipathy toward Israel holds sway.

The Egyptian cabinet issued a statement on Saturday demanding an apology and an investigation, and saying the ambassador to Israel would be recalled. Thousands of protesters gathered outside the Israeli Embassy in Cairo, burning an Israeli flag and demanding the ambassador be expelled and the embassy closed.

The protests at the embassy continued on Sunday night, but the crowd had dwindled to several hundred. They waved flags, launched fireworks at the building and chanted slogans, including “Close the embassy” and “Arab blood is not cheap.” Some expressed anger that the Egyptian military government had not taken sterner measures against Israel.

Egyptian soldiers took up positions in armored cars nearby, but kept their distance in an apparent attempt to avoid confrontations.

The noisy demonstration contrasted sharply with the remarkable official silence from both governments.

Egyptian authorities made no official statements on Sunday, and there were conflicting reports about whether the government intended to follow through with the announced plan to recall its ambassador to Israel. A statement about recalling the ambassador was removed from the cabinet’s Web site over the weekend, shortly after being posted.

In Israel, Prime Minister Benjamin Netanyahu refrained from making any public remarks over the weekend.

Israeli officials have also stopped publicly criticizing Egypt for the lawlessness in the Sinai Peninsula, where Israel says the militants crossed the border to carry out their multi-pronged attack on Thursday. Earlier statements to that effect fueled the initial fury in Cairo, and the Egyptian cabinet expressed anger at the Israeli comments.

Israel’s president, Shimon Peres, expressed regret on Sunday for the Egyptian deaths, building on a similar statement by Defense Minister Ehud Barak on Saturday.

“I regret that Egyptian soldiers fell and am certain that no Israeli would want to see Egyptian soldiers killed,” the statement by Mr. Peres said. “I convey my condolences to the Egyptian people and the soldiers’ families.”

Among the conciliatory official statements, one dissonant note came from the Arab League, which condemned Israel. According to the Egyptian official news agency MENA, the group issued a statement saying that it held Israel “fully responsible.”

The anger on the streets of Cairo was evidence that the fall of President Hosni Mubarak in February has ushered in a new era in which Egyptians critical of their country’s 1979 peace treaty with Israel are far more willing to give public voice to anti-Israel sentiments. So far it is unclear how the military government will respond.

The diplomatic challenge it faces was perhaps brought into sharpest relief on Sunday by the instant celebrity accorded Ahmed el-Shahat, now known on Twitter as #Flagman.

Mr. Shahat scaled the multi-story Israeli embassy building in the early hours of Sunday, removed the Israeli flag and replaced it with an Egyptian one. He brought the blue and white Israeli standard down with him, where it was burned and he was celebrated as a local hero.

After video of the climb appeared on YouTube and circulated on Twitter, his fame circled the globe.

“My happiness is indescribable,” he told the Jazeera Live Egypt television channel in a telephone interview. “I did something that millions of Arabs want to do, to bring down the Israeli flag. This is a chance to put more fear in the hearts of the Zionists.”