Protesters chant around a fire during a protest demanding the release of hostages still held in Gaza and against the government of Israeli Prime Minister Benjamin Netanyahu, outside The Kirya, the area where Israel's armed forces have their headquarters, March 16, 2024, in Tel Aviv, Israel. ALEXI J. ROSENFELD/GETTY

There was growing optimism Monday around talks of a possible new cease-fire in the Gaza Strip, with both Israel and Hamas returning to the table to discuss a truce that would see more Israeli hostages released in exchange for the release of Palestinian prisoners.

CBS News chief foreign affairs correspondent Margaret Brennan said the Biden administration is hoping to leverage a possible six-week cessation of violence into a longer-term pause, and it has been pushing Israeli leader Benjamin Netanyahu to scale-down plans for an all-out ground offensive in the packed southern Gaza city of Rafah.

Israel's handling of the war, which was sparked by Hamas' unprecedented Oct. 7 terrorist attack that saw the militants kill some 1,200 people and kidnap about 240 others across southern Israel, has created a rift between the U.S. and Netanyahu's government.

President Biden spoke to Netanyahu on the phone on Monday, their first conversation in more than a month. White House national security adviser Jake Sullivan said the president told Netanyahu that he was "deeply concerned about the prospect of Israel conducting major military operations in Rafah," given its large civilian population and its proximity to Egypt.

"Our position is that Hamas should not be allowed a safe haven in Rafah or anywhere else," Sullivan said at the White House briefing. "But a major ground operation there would be a mistake. It would lead to more innocent civilian deaths, worsen the already dire humanitarian crisis, deepen the anarchy in Gaza and further isolate Israel internationally."

Sullivan said Netanyahu agreed to send a delegation of intelligence and military officials to Washington to hear the White House's proposal for a different approach, one that would include targeted strikes against Hamas officials in Rafah without the need for an all-out ground offensive.

"The key goals Israel wants to achieve in Rafah can be done by other means," Sullivan said.

The national security adviser added that the U.S. is continuing to push for a cease-fire and hostage deal, which he called an "urgent priority" while acknowledging that an agreement "has been more elusive than we would have hoped."

European Union says Israel "provoking famine" in Gaza
The European Union has also sharply criticized Netanyahu, with the bloc's foreign policy chief Josep Borrell saying at a humanitarian conference over the weekend that Gaza was "no longer on the brink of famine, we are in a state of famine, affecting thousands of people."

Starvation, Borrell said, "is used as a weapon of war. Israel is provoking famine."

Israeli Foreign minister Yisrael Katz responded with a social media post insisting that "Israel allows extensive humanitarian aid into Gaza by land, air, and sea for anyone willing to help."

Katz also reiterated an Israeli allegation that Hamas militants have been "violently disrupting aid convoys" — a charge U.S. officials said recently that they had no evidence to back up.

The Hamas-run Ministry of Health says more than 31,500 people have been killed in Gaza since the war started. It does not distinguish between civilian and combatant deaths, but with tens of thousands of people dying in Gaza from both the fighting and from hunger, some senior U.S. leaders appeared to lose their patience last week, and the tension between Israel and its closest ally only seemed to grow over the weekend.

Senate Majority Leader Chuck Schumer, America's highest-ranking Jewish elected official, stunned Israel late last week by calling for the country to hold new elections and saying Netanyahu had "lost his way."

The veteran Israeli politician fired back, telling Fox News over the weekend blasting Schumer's remarks as "wholly inappropriate."

"We're not a banana republic," Netanyahu protested. "The people of Israel will choose when they'll have elections, who they elect, and it's not something that will be foisted upon us."

The Biden administration, along with many other Western governments and international aid organizations, has repeatedly warned Israel against launching its promised full-scale offensive in Rafah. The city, a longtime Hamas stronghold on Gaza's southern border with Egypt, has over the last five months of war become a refuge to an estimated 1.5 million people, most of them displaced from elsewhere in the decimated Palestinian territory.

Despite the heavy international pressure against sending forces into the city, Netanyahu refused to back down over the weekend, at least publicly.

"We're within reach. We should do it. We're going to do it while we enable the civilian population in Rafah to leave, as we've done up to now," he told Fox News. "But we have to finish the job."

Deadly clashes at Gaza's Al-Shifa hospital
On Monday morning, meanwhile, in an ongoing operation, Israel said it had captured more than 80 fighters and killed at least 20 terrorists at Gaza's Al-Shifa hospital, which was the scene of fierce battles earlier in the war. Sources on the ground told CBS News that some 30,000 displaced people were sheltering at the hospital complex, plus dozens of patients and medical teams.

Harrowing images emerged from the scene of a purported Israeli strike near the hospital, with the body of a small child seen laying on the rubble of a destroyed building with dust still hanging in the air.

Hamas acknowledged battling Israel Defense Forces near the health facility. In a statement, the IDF said "20 terrorists have been eliminated" during its ongoing "precise operations in the Shifa hospital."

The IDF said it also found "numerous weapons" in the hospital, which it called "further evidence of Hamas' systematic abuse of hospitals and civilian infrastructure for its terrorist activities."

Israeli protesters fume at Netanyahu, demand hostages' release
The humanitarian cost of the war, and the failure of Netanyahu's government to free the more than 100 hostages still believed to be captives in Gaza, has all been too much to tolerate for some Israelis, including dozens who staged another protest over the weekend, and who appeared to share the growing sense of international frustration with the war.

"This says: 'Elections now,'" protester Ori Orman said of the sign he was carrying. "I believe that after such a disaster... even if you don't think Benjamin Netanyahu is directly responsible, because of the fact that he is the prime minister, I think he should step down."

That doesn't mean the entire Israeli public is against the war. Most Israelis still say they support the fight against Hamas. What many don't still support, however, is Netanyahu and the way he's prosecuting that war.

The Oct. 7 massacre and kidnappings happened on his watch, and for that, many people say he, too, has blood on his hands.

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