Secretary of State Antony J. Blinken on Friday urged Israel’s leaders to take steps to protect Palestinian civilians in Gaza and allow more humanitarian aid to enter the besieged territory, amid a war that has killed thousands of people and inflamed the Middle East.

But soon after meeting with Mr. Blinken, Prime Minister Benjamin Netanyahu of Israel appeared to rebuff the Biden administration’s call for a series of “humanitarian pauses” to allow more deliveries of badly needed food, water, medicine and other supplies and facilitate the release of hostages held by Hamas. Mr. Netanyahu said that any cease-fire would be contingent on the release of Israeli hostages, many of them children, abducted in a deadly attack on Oct. 7.

“I have made clear that we are continuing forcefully, and that Israel refuses a temporary cease-fire that does not include the release of our hostages” held by Hamas, he said. He also stood fast on Israel’s refusal to let fuel enter Gaza, even as it allows limited shipments of other vital supplies.

Mr. Blinken told reporters in Tel Aviv that the United States stood “in solidarity” with Israel, but said that in meetings with Mr. Netanyahu and other Israeli leaders, he had emphasized that “it matters” how Israel conducts its campaign to defeat Hamas, the militant group that controls Gaza. The Oct. 7 attack, orchestrated by Hamas, killed more than 1,400 people and seized more than 200 hostages, according to the Israeli government.

“We provided Israel advice that only the best of friends can offer on how to minimize civilian deaths while still achieving its objectives of finding and finishing Hamas terrorists,” Mr. Blinken said. He said they had discussed “concrete steps” to protect civilians, and also “tangible steps” to allow more aid to enter Gaza, but did not elaborate on either topic.

While President Biden continues to declare unambiguous support for Israel, saying the country has a right to defend itself, concern has been growing within his administration about the mounting Palestinian death toll — more than 9,200, according to the Hamas-controlled Gazan health ministry — worsening humanitarian conditions and physical destruction brought on by the Israeli bombing campaign and week-old ground invasion.

With Israel’s ground forces pushing into Gaza’s largest city and its airstrikes killing and wounding many more Palestinians every day, anger is rising across the region even as Mr. Blinken tries to keep Israel’s adversaries from broadening the war. Fighting between Israeli troops and the armed group Hezbollah has escalated along Israel’s northern border with Lebanon, and Hezbollah’s leader, Hassan Nasrallah, gave a fiery speech on Friday denouncing both Israel and the United States.

After meeting with President Isaac Herzog of Israel, Mr. Blinken said: “It is very important that, when it comes to the protection of civilians who are caught in the crossfire of Hamas’s making, that everything be done to protect them and to bring assistance to those who so desperately need it.”

But he repeated that the United States remained steadfastly behind Israel. He told reporters that he had been shown additional images and videos collected by the Israeli government documenting the slaughter of civilians on Oct. 7. “It remains almost beyond the human capacity to process, to digest,” Mr. Blinken said.

Pauses in the fighting would allow for humanitarian aid to be distributed, would facilitate hostage negotiations, and would let more people exit Gaza through the Rafah border crossing into Egypt, the administration has said. The first several hundred dual nationals, foreigners and staff members of international organizations were allowed to leave this week.

More than a million Gazans have been displaced by the war, and the territory, blockaded by Israel, is dangerously low on food, fuel, water and medicines. After a complete cutoff of outside aid in the first two weeks of the war, scores of trucks with aid are now moving daily into Gaza.

“That’s significant progress in the space of a couple of weeks — but it’s also insufficient,” Mr. Blinken said, echoing the view of the United Nations and aid groups.

Mr. Blinken left Israel for talks in Amman, Jordan, with Jordanian leaders and other regional partners about securing the release of hostages taken by Hamas, and about preventing the war from expanding.

Michael D. Shear, Cassandra Vinograd and Aaron Boxerman contributed reporting.