Israeli forces were battling Palestinian terrorists across the Gaza Strip on Sunday, including in parts of the devastated north that the military said it had cleared months ago, where Hamas has exploited a security vacuum to regroup.

Israel has portrayed the southern Gaza city of Rafah as Hamas’ last stronghold, saying it must invade in order to succeed in its goals of dismantling the group and returning scores of hostages. A limited operation there has expanded in recent days, forcing some 300,000 people to flee and drawing warnings from Egypt, where an official said it is putting the country’s decades-old peace treaty with Israel at risk.

But the rest of the war-ravaged territory seems to provide ample opportunities for Hamas. Israel has yet to offer a detailed plan for postwar governance in Gaza, saying only that it will maintain open-ended security control over the coastal enclave, which is home to some 2.3 million Palestinians.

The ongoing fighting comes as Israel marks its Memorial Day for fallen soldiers and victims of attacks beginning at sundown Sunday, with an official ceremony and smaller events the following day at military cemeteries across the country. The solemnity is then abruptly interrupted by the fanfare of Independence Day, which begins Monday evening.

Prime Minister Netanyahu has rejected postwar plans proposed by the United States for the Palestinian Authority, which administers parts of the Israeli-occupied West Bank, to govern Gaza with support from Arab and Muslim countries. Those plans depend on progress toward the creation of a Palestinian state, something to which Mr. Netanyahu’s government is deeply opposed.

With the two close allies divided, Gaza has been left without a functioning government, leading to a breakdown in public order and allowing Hamas to reconstitute itself in even the hardest-hit areas.

Palestinians reported heavy Israeli bombardment overnight at Jabaliya and other areas in the northern Gaza Strip, which has suffered widespread devastation and been largely isolated by Israeli forces for months.

Residents said Israeli warplanes and artillery struck across the town and the Zeitoun area east of Gaza City, where troops have been battling Palestinian militants for over a week. They have called on tens of thousands of people to relocate to nearby areas.

First responders with the Palestinian Civil Defense said they were unable to respond to multiple calls for help from both areas, as well as Rafah, on the southern edge of Gaza. Israeli troops have been battling militants there since the army seized the nearby border crossing with Egypt last week.

Rear Admiral Daniel Hagari, the top Israeli military spokesman, said troops are fighting in all parts of Gaza, “in areas where we have not yet operated and in places where we have.”

He said that in addition to Jabaliya and Zeitoun, forces were also operating in Beit Lahiya and Beit Hanoun, towns near Gaza’s northern border with Israel that were heavily bombed in the opening days of the war.

The military “is now going into Jabaliya for the second time and into Zeitoun for the third time, and it will continue to go in and out,” columnist Ben Caspit wrote in Israel’s Maariv daily, channeling the growing frustration felt by many Israelis more than seven months into the war.

“Hamas’ regime cannot be toppled without preparing an alternative to that regime,” he wrote, drawing comparisons with the American wars in Iraq and Afghanistan. “The only people who can govern Gaza after the war are Gazans, with a lot of support and help from the outside.”

Five Israeli soldiers were killed in Zeitoun on Friday, and Palestinian terrorists fired a barrage of 14 rockets toward the Israeli city of Beersheba that night. Another rocket launched overnight damaged a home in the Israeli city of Ashkelon, the military said Sunday.

The United Nations’ agency for Palestinian refugees, the main provider of aid in Gaza, meanwhile said 300,000 people have fled Rafah since the operation began there. Most are heading to the heavily damaged nearby city of Khan Younis or Mawasi, a crowded tent camp on the coast where some 450,000 people are already living.

Rafah was sheltering some 1.3 million Palestinians before the Israeli operation began, most of whom had fled fighting elsewhere in the territory.

Israel has now evacuated the eastern third of Rafah, and Admiral Hagari said dozens of militants had been killed there as “targeted operations continued.”

Rafah borders Egypt near the main aid entry points, which are already affected. Israeli troops have captured the Gaza side of the Rafah crossing, forcing it to shut down. Egypt has refused to coordinate with Israel on the delivery of aid though the crossing because of “the unacceptable Israeli escalation,” the state-owned Al Qahera News television channel reported, citing an unnamed official.

A senior Egyptian official told The Associated Press that Cairo has lodged protests with Israel, the United States and European governments, saying the offensive has put its peace treaty with Israel — a cornerstone of regional stability — at high risk.

President Biden has said he won’t provide offensive weapons to Israel for Rafah. On Friday, his administration said there was “reasonable” evidence that Israel had breached international law protecting civilians — Washington’s strongest statement yet on the matter.

Israel rejects those allegations, saying it tries to avoid harming civilians. It blames Hamas for the high toll because the militants fight in dense, residential areas using the civilians as human shields.