The Biden administration has told the Israeli government that it wants the country to end its large-scale ground campaign in Gaza and transition to a more targeted phase of , two U.S. officials familiar with the discussions told NBC News.

The officials stressed that White House national security adviser did not specify a timetable for this new phase of the war during his meeting Thursday with Israeli Prime Minister Benjamin Netanyahu.

At Thursday's White House press briefing, National Security Council spokesman John Kirby said Sullivan spoke with Netanyahu about "the next phase of Israel's military campaign, and he asked hard questions, as we have been doing, about what all that could look like."

Kirby said that Sullivan "also discussed efforts Israel's now undertaking to be more surgical and precise in their targeting and efforts that they are taking to help increase the flow of aid."

The push comes as the death toll in the Gaza Strip approaches 20,000 — two-thirds of them women and children — according to local health officials. About 1,200 people in Israel were killed in the Oct. 7 Hamas attack, according to the Israel Defense Forces.

Sullivan had "a heavy discussion" about civilian protection with Israeli officials during his trip to the region, a senior administration official said Thursday on a call with reporters.

"There was a discussion in these meetings — and also in our prior meetings and in calls between the president and the prime minister — on kind of shifts and emphasis from...high intensity clearance operations, which are ongoing now, to ultimately lower-intensity focus on high-value targets, intelligence-driven raids and those sorts of more-narrow surgical military objectives," the senior administration official said.

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Israeli officials have briefed U.S. officials on their "thinking of potential timeframes," the official said.

"I think the Israelis had ideas for the military campaign very early which we found problematic, and I think the president's visit out here very early in the crisis, discussed that in some detail," the official said. "And the ground campaign was adjusted based upon some of our advice, some of our recommendations, with the recognition that this ultimately is not our war."

NBC News has that U.S. officials have warned Israeli officials privately to show restraint and avoid mass civilian casualties. The Israeli military has previously warned Palestinians to evacuate neighborhoods ahead of bombardments, but Palestinians there's no safe place to go.

U.S. officials on Thursday also discussed with Israeli counterparts "the protection of hospitals, even when those hospitals are being used by Hamas," the senior administration official said.

At an unrelated event on Thursday, Biden was asked whether he wanted Israel to scale back its assault on Gaza. He responded: "I want them to be focused on how to save civilian lives. Not stop going after Hamas — but be more careful."

Earlier Thursday, before meeting with Sullivan, Israeli Defense Minister Yoav Gallant said that the war against Hamas would "last more than several months."

"That's consistent with what they've been saying since almost the very beginning, that this could take some time," Kirby said at the White House press briefing. "We're not dictating terms to the Israelis about how long it has to take."

About 100 hostages are still being held in Gaza, the senior administration official said Thursday.

U.S. officials acknowledge it will take months for Israel to take out Hamas leaders, an effort that will continue even if the high-intensity phase of the war moves to a more surgical one. The debate over the pace of the war comes after Biden warned earlier this week in a speech to campaign donors that Israel was losing global support because of "indiscriminate bombing."