As the violence between the Israeli military and Palestinian militants in Gaza stretched into a fifth day on Saturday, Egyptian-led mediation efforts for a cease-fire were unable to stop the fighting, making this round of clashes among the longest in recent years.

The fighting has remained contained because the militant group, Palestinian Islamic Jihad, has failed to draw in Hamas — the more powerful Islamic militant organization that controls Gaza — or any other major faction. The Islamic Jihad fighters, alone on the battlefield, have suffered crushing blows.

Some experts attribute the stamina of Islamic Jihad — which Israel, the United States and many other Western countries classify as a terrorist organization — to the fact that, unlike Hamas, it does not bear any responsibility for Gaza’s largely impoverished population of more than two million people. Instead, it is focused only on its long-term goal of replacing Israel with an Islamic state.

“It exists just for one purpose: to fight and ‘liberate’ the country,” Zakaria al-Qaq, a Palestinian expert in national security based in East Jerusalem, said of Islamic Jihad.

“They have no ministerial positions or parliamentary seats to keep and no privileges other than to die” he said, adding that the group was gaining the respect of many Palestinians, who sympathize with the Gazans living under a strict land, air and sea blockade imposed by Israel and Egypt.

Israel also maintains that Iran, Islamic Jihad’s patron, has been setting the agenda while the group’s leaders live in exile. Rear Adm. Daniel Hagari, the chief spokesman for the Israeli military, said this past week that the group’s leaders, “living in hotels in Beirut and Damascus and driving Mercedes” while on the Iranian payroll, were “OK with Gaza bleeding.”

Previous rounds of fighting between Israel and Islamic Jihad — in April, in August last year and in November 2019 — were all over in about 50 hours or less.

But in a television interview in October, Ziyad al-Nakhalah, the leader of Palestinian Islamic Jihad in exile, said the group had made a “strategic mistake” two months earlier in agreeing to a cease-fire after 50 hours, under local and regional pressure. He said they could have continued fighting and achieved “concrete results on the ground.”

This time, Israel has argued that it is ready for a cease-fire with no preconditions, but it has also said that it is ready to continue with its offensive. For its part, Islamic Jihad cited “great loyal popular support” on Saturday and said that “the resistance has prepared itself for months of confrontation.”

Two significant events on the calendar in the coming week have the potential to draw broader Arab support for the group’s cause.

On Monday, Palestinians and their supporters will mark the 75th anniversary of the Nakba, or “catastrophe” in which hundreds of thousands of Palestinian refugees fled or were expelled from their homes in the war surrounding Israel’s creation in 1948 and hundreds of Palestinian villages were destroyed in what is now Israel. Then, later this coming week, tens of thousands of Israeli nationalists are expected to march through the Muslim Quarter of Jerusalem’s Old City with flags in an annual parade commemorating Israel’s capture of East Jerusalem in the 1967 war.

After firing rockets toward Jerusalem on Friday, Dawoud Shehab, a spokesman for Islamic Jihad, told a local Arabic news outlet, “The battle is approaching the time of the flag march — that is what spurs us on to continue.”

The warring sides traded fire again overnight and on Saturday. The Israeli military said it had struck mortar-shell- and rocket-launching sites belonging to Islamic Jihad as well as what it described as two of the group’s command centers. And sirens continuously sounded in southern Israel, warning of barrages of incoming projectiles.

Over the past five days, Islamic Jihad has fired more than 1,000 rockets and mortar rounds toward Israel, and Israel has struck more than 250 targets affiliated with the group in Gaza, according to data released by the military. The Israeli authorities also said that the group had fired dozens of mortar shells toward areas near the border crossings between Israel and Gaza, preventing their opening for the passage of people and goods.

The Palestinian Ministry of Health has reported at least 33 people killed in Gaza, many of them civilians, since the campaign began and more than 100 injured. In Israel, an older woman was killed on Thursday by a rocket launched from Gaza that struck an apartment block in central Israel. Israel’s ambulance service has reported eight injured by shrapnel and debris, including three whom it said were wounded on Saturday, two of them severely. According to the Israeli news media, two of the three were Palestinian workers from Gaza.

Israeli officials said the decision to launch the offensive against leaders of Islamic Jihad was made on May 2, the day that the group fired more than 100 rockets and mortar shells at southern Israel after the death in Israeli custody of a Palestinian hunger striker, Khader Adnan, who was protesting his detention. Mr. Adnan was an Islamic Jihad leader from the occupied West Bank. That night, Israel carried out some initial airstrikes in Gaza that killed one man.

Israeli officials said the campaign that began on Tuesday was aimed at weakening Islamic Jihad,, an objective they achieved in the first seconds of the campaign, and restoring stability to the area. The opening strikes killed three of Islamic Jihad’s top commanders and 10 civilians, including children, according to Palestinian health officials. Three more of the group’s key commanders were killed in subsequent strikes this week.

The United States has backed Israel’s right to defend itself against indiscriminate rocket fire by Islamic Jihad, while also stressing the urgency of reaching a cease-fire agreement.

Islamic Jihad has presented several conditions for a cease-fire, including an Israeli commitment to halt assassinations; the release of Mr. Adnan’s body for burial; and the cancellation of the Jerusalem flag parade — conditions that Israel has refused.

Egypt presented a new proposal on Friday night for a cease-fire with no preconditions, according to a diplomat informed about the talks. But on Saturday, the guns were still doing the talking.

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