Tel Aviv — Israeli Prime Minister Benjamin Netanyahu was under rising pressure Monday from all sides over his country’s ongoing war against Hamas in the Gaza Strip. Far-right members of Netanyahu’s own cabinet have threatened to drop their support for his coalition government if he accepts a cease-fire deal with Hamas, but the U.S. and many Israelis are pushing him to strike an agreement to bring the remaining hostages home from Gaza and wind down the devastating war in the Palestinian territory.

Those calls for a cease-fire got renewed impetus by the release over the weekend of another Hamas propaganda video showing two hostages, including Israeli-American national Keith Seigel, still alive.

The new week has brought a flurry of diplomatic activity in the region, including a visit by Secretary of State Antony Blinken, in a last-ditch attempt to secure a cease-fire agreement ahead of a possible Israeli ground operation in the southern Gaza city of Rafah, where some 1.4 million Palestinians have sought shelter in desperate conditions.

A Hamas delegation was expected to deliver the group’s response on Monday to the latest proposal for a long-sought truce and hostage release deal.

In Saudi Arabia for a meeting with Gulf region counterparts, meanwhile, Blinken said Monday that a cease-fire would be the most effective way to ease the humanitarian crisis in Gaza. But he stressed that civilians caught in the middle of the war can’t afford to wait for that to happen, and he urged Israel “to take the necessary steps to meet the needs of civilians.”

Blinken acknowledged “measurable progress in the last few weeks, including the opening of new [border] crossings and increased volume of aid delivery to Gaza and within Gaza, and the building of the U.S. maritime corridor, which will open in the coming weeks. But it is not enough,” he said.

He said President Biden was adamant that Israel should take more specific, concrete, measurable steps to better address humanitarian suffering, civilian harm and the safety of aid workers in Gaza — including in his most recent call with Netanyahu on Sunday.

According to Gaza’s Hamas-run Health Ministry, more than 34,000 people — mostly women and children — have been killed in the enclave since the war began. It was sparked by Hamas’ unprecedented Oct. 7 terrorist attack on Israel, which saw the group kill some 1,200 people and take about 240 others hostage.

United Nations humanitarian agencies have also acknowledged an increase in aid flowing into Gaza, but they continue to warn that tens of thousands of people face possible famine conditions in the territory, and the uptick in aid hasn’t been enough to avert that.

The challenge for Netanyahu has been weighing the fate of about 130 remaining hostages — including five U.S. nationals still believed to be alive — and the rising pressure over the war’s impact on Palestinian civilians, against his stated mission to destroy Hamas. He’s said a Rafah incursion is the only way to meet that goal, as Hamas still has combat units hiding out in the city.

Calls from the families of the remaining captives to strike a deal have grown louder and angrier, however. They’ve led regular, massive rallies on the streets of Israel, accusing Netanyahu of failing the hostages. More than once the protests have ended in scuffles with police.

There’s pressure for a cease-fire, too, from college campuses across the U.S. — Israel’s most important ally and benefactor — and from parallel protests taking shape on European university campuses. The anti-war demonstrations have not gone unnoticed by displaced Palestinian students in Rafah, whose education came to an abrupt halt on Oct. 7.

“What gives us a glimpse of hope is that we weren’t left alone,” student Renad Anaan told CBS News at a camp for displaced people, “and that goes for efforts made by the students at universities in America.”

“I salute them, the American university students who are protesting against Netanyahu’s government and the American government. That’s kind of them and I admire them for that,” said Fida Afifi, whose university course in Gaza City was disrupted by the war. She told CBS News she was “calling on the world’s students to rise against the government.”

Israel has made a concerted effort in recent days to show it’s stepping up aid distribution in Gaza, and the IDF released video over the weekend showing the floating pier being built by the U.S. military just off envlave’s Mediterranean coast. Officials have said it will be completed in early May, creating another new route for help to reach people who desperately need it.

There’s hope that a cease-fire deal, or even progress toward one, could delay or even scuttle the plans for Netanyahu’s promised invasion of Rafah. But in the meantime, the threat of ground warfare in the crowded city continues to hang over the students and the tens of thousands of other civilians sheltering in Rafah.

Much of the rest of Gaza lies in ruin — destruction on a scale that has left entire towns and cities uninhabitable.

Nowhere is really safe. Even in Rafah, the Israel Defense Forces carry out daily air and missile strikes. Monday morning, amid the renewed talk of a possible cease-fire, there were three new strikes on the city. At least five more children were among the dead, according to health officials in the Hamas-run territory.

Both humanitarian air drops and Israel’s bombardment continued over the weekend, and Palestinians eking out survival in the tent city that’s grown in and around Rafah never know whether planes flying above carry the threat of death, or the promise of life saving aid.

CBS News’ Tucker Reals contributed to this report.