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National security adviser Jake Sullivan.
CNN  — 

The United States is communicating to the Israeli government “at the highest levels” the importance of protecting civilian lives in Gaza, US national security adviser Jake Sullivan said Sunday, even as he repeatedly declined to say whether Israel was going about its war the right way.

They’re the ones making decisions, they’re the ones conducting the operations,” Sullivan told CNN’s Jake Tapper on “State of the Union,” declining to openly criticize any aspect of the new military effort.

President Joe Biden spoke with Israeli Prime Minister Benjamin Netanyahu later Sunday – their first known conversation since Israel expanded its ground operations – about the need for the continued flow of aid into Gaza and stressed the importance of protecting civilians lives, according to the White House.

Biden reiterated his support for Israel to defend itself but said the country needs to do so “in a manner consistent with international humanitarian law that prioritizes the protection of civilians,” according to the White House. He also called for significantly increasing the flow of humanitarian assistance into Gaza and discussed efforts to locate hostages held by Hamas.

The US applied pressure on Israel to restore connectivity in Gaza after phone and internet service were badly disrupted late last week, according to a senior US official.

The near-total blackout – which left civilians, aid groups and journalists struggling to communicate with the outside world – came amid heavy Israeli bombardment of the enclave. Service appeared to be gradually restored Sunday.

Speaking to MSNBC on Sunday, Sullivan underscored the importance of communications networks in Gaza, saying, “We do feel strongly that the restoration of that communications was a critical thing.”

“Because aid workers need to be able to communicate, civilians need to be able to communicate, and of course, journalists need to be able to document what is happening in Gaza to report it to the wider world,” he said.

The assault on Gaza has left thousands of Palestinian civilians dead and worsened the humanitarian crisis in the enclave. Aid has been slow to enter, and civilians, including hundreds of Americans, have been unable to leave. While some aid has made its way to Gaza, humanitarian workers say it’s a fraction of what’s required for the 2.2 million people crammed into Gaza under a blockade imposed by Israel and Egypt.

More than 200 hundred hostages also remain held by Hamas on the strip, according to officials, and securing their release could be complicated by the expanded operation.

Sullivan told CNN that Israel was solely responsible for its military operations. “I’m not going to react to every strike, every move that they make,” he said.

But Sullivan did indicate that tougher conversations were being held behind the scenes between senior US and Israeli officials — including Biden and Netanyahu — about the scope and intent of Israel’s military efforts in Gaza.

“We have had numerous conversations – from the prime minister and the president on down, and certainly among military leaders and their counterparts – about Israeli military objectives and about the steps that they have taken and intend to take to achieve those objectives,” he said.

“We’ve asked them hard questions, the same hard questions that we would ask ourselves if we were seeking to conduct an operation to take out a terrorist threat,” he went on. “We’ve pressed them on questions like objectives and matching means to objectives, about both tactical and strategic issues associated with this operation.”

Sullivan said Hamas was “making life extremely difficult for Israel” by using civilians as human shields and placing its rocket infrastructure among civilian populations.

“That creates an added burden for Israel. But it does not lessen Israel’s responsibility under international humanitarian law to distinguish between terrorists and civilians, and to protect the lives of innocent people,” he said.

The US remains in “hourly contact” with its partners in the region to try securing the release of hostages, Sullivan said. CNN has previously reported on intensifying efforts brokered by the government of Qatar to secure a large number of hostages held by Hamas.

“The Hamas terrorists have not been forthcoming about allowing these hostages to go, but we believe that there can still be a pathway to get them released and we’re going to work tirelessly to make that happen,” Sullivan said. “And even though we’ve started to see Israel moving on the ground, that has not changed our basic view that this has to remain a paramount priority that we have to keep working at.”

Sullivan blamed Hamas for the inability of Americans stuck in Gaza to leave through the Rafah crossing into Egypt, saying the Egyptians were prepared to allow Americans and other foreign nationals to enter.

“Hamas had been preventing their departure and making a series of demands. I can’t go through those demands in public. But that is the subject of the discussions in the negotiations that are ongoing,” he said.

Sullivan also repeated calls first made by Biden at a news conference Wednesday on Israeli settlers in the West Bank to cease violence against Palestinians.

“We believe that Prime Minister Netanyahu does have a responsibility to rein in the extreme settlers on the West Bank, who are, as President Biden put it a few days ago, pouring fuel on the fire,” he said, adding: “We expect over time to see the Israeli government step up on this.”

This story has been updated with additional information.

CNN’s Aileen Graf contributed to this report.