For two months, President Biden has strongly backed Israel’s right to defend itself after the Oct. 7 terrorist attack by Hamas, in effect banking credibility with Jerusalem to be spent on moderating its response. But as Israeli forces push into southern Gaza, the question is when Mr. Biden’s account will be drained and the checks start to bounce.

Administration officials insist they have meaningfully influenced Israel’s actions over the last few weeks thanks to the president’s approach, and continue to do so. But the nightly phone calls between Washington and Jerusalem have turned increasingly fraught and the public messages by some of the administration’s top officials have become sharper in recent days.

The friction was evident on Tuesday when the State Department imposed visa bans on Israeli settlers in the West Bank who have committed violence against Palestinians, a rebuke to Prime Minister Benjamin Netanyahu for not doing more to restrain such attacks far from the action in Gaza. At the same time, in defiance of Washington’s warnings, Mr. Netanyahu said that Israel’s military would maintain security control over Gaza long after defeating Hamas.

The stakes are high for both sides. Mr. Netanyahu’s Israel needs the Biden administration’s support to continue resupplying its forces and to shield it from international pressure from other corners, including the United Nations. Mr. Biden, for his part, has become so closely associated with Israel that he effectively owns its military operation and has absorbed withering political attacks, especially from the left wing of his own party, which has accused him of enabling mass slaughter of civilians.

“The real question is: How do you, on the one hand, allow a sovereign nation like Israel to go after terrorist targets while, on the other hand, have them do so in a way that minimizes the harm to civilians?” Jake Sullivan, the president’s national security adviser, told reporters this week. “And that’s really where the rubber hits the road in all of this.”

For the moment, Mr. Biden has left it to subordinates to deliver the tougher messages in public. In recent days, Vice President Kamala Harris declared that “Israel must do more to protect innocent civilians” and sent her own national security adviser to Israel to convey the concerns of Arab leaders she met with during a trip to Dubai.

Secretary of State Antony J. Blinken said it was imperative for the United States that “the massive loss of civilian life and displacement on the scale that we saw in northern Gaza not be repeated in the south” and Defense Secretary Lloyd J. Austin III warned Israel that “if you drive them into the arms of the enemy you replace a tactical victory with a strategic defeat.”

Mr. Biden himself, though, has measured his words and said little about Israel’s military assault on southern Gaza since it began a few days ago. At a campaign fund-raiser in Boston on Tuesday, he focused again on the atrocities committed by Hamas when it killed 1,200 people and seized another 240 as hostages.

“Over the past few weeks, survivors and witnesses of the attacks have shared the horrific accounts of unimaginable cruelty,” Mr. Biden told donors. “Reports of women raped — repeatedly raped — and their bodies being mutilated while still alive — of women corpses being desecrated, Hamas terrorists inflicting as much pain and suffering on women and girls as possible and then murdering them. It is appalling.”

He added that “the world can’t just look away,” and should “forcefully condemn the sexual violence of Hamas terrorists without equivocation.” Mr. Sullivan and John F. Kirby, the National Security Council spokesman, in recent days have likewise stressed the culpability of Hamas and support for Israel’s response while urging care for civilians.

The disparity reflects to some extent traditional good-cop-bad-cop diplomacy, where a president leaves it to others to lay down a harder line while he remains more removed. Aides maintain that “there’s no daylight,” as Mr. Sullivan put it, between the president and his team even if their emphasis sounds different. In private, aides said, Mr. Biden has been just as forceful with Mr. Netanyahu as his vice president and cabinet secretaries.

“The president wants to avoid criticizing Bibi in public to the farthest extent possible,” said Martin S. Indyk, a former Middle East special envoy, using Mr. Netanyahu’s nickname. “However, having Vice President Harris speak out so clearly is the closest you can get — one degree of separation.” Likewise, he said, with Mr. Blinken and Mr. Austin.

“I see it as a very carefully calibrated public campaign made necessary by their concern that the message is not getting through in private,” added Mr. Indyk, who worked alongside Mr. Biden and Mr. Blinken in President Barack Obama’s administration. “I don’t remember a time when so many senior officials spoke out in concert with such a clear warning to Israel.”

Critics of Mr. Biden’s embrace of Israel were unimpressed, suggesting he was empowering his team to publicly chide Israel without actually doing anything to stop the war.

“The Biden administration is trying to have its cake and eat it too,” said Sarah Leah Whitson, executive director of Democracy for the Arab World Now, an advocacy group. “It wants to respond to growing public demand to rein in Israeli atrocities, while satisfying donor demands for unconditional military support for Israel. Ultimately, the Israelis will only pay attention to what the Biden administration actually does, not just what it says.”

On the other side of the political spectrum, some conservatives faulted Mr. Biden for undermining his own stated support for Israel.

“Up until a week ago, the Biden administration had been pretty solid in its support of Israel’s stated goal of destroying Hamas,” said Enia Krivine, an Israel specialist at the Foundation for Defense of Democracies. “The administration gave Israel about eight weeks of time and space and now is beginning to assert conditions for continued support.”

She added that Israel wants “to keep the U.S. on its side for as long as possible” but may find it impossible to fully accede to the Biden administration’s appeals and so “Jerusalem may eventually have to decide between appeasing Washington and fully accomplishing the goals of the war.”

Mr. Biden has made a point of regularly calling Mr. Netanyahu and continues to send a parade of officials to meet with the prime minister and his officials. Philip H. Gordon, the vice president’s national security adviser, was in Tel Aviv on Tuesday to pass along the anxiety of the Arab leaders Ms. Harris had met in Dubai and their insistence on an eventual political path to Palestinian self-rule.

Mr. Gordon was focusing on the day-after questions of what will happen in Gaza once Israel completes its war on Hamas. After meetings with Israeli officials, Mr. Gordon was scheduled to head to Ramallah on Wednesday to consult with leaders of the Palestinian Authority, which partially runs the West Bank. The Palestinian Authority resists Israeli settlements and compensates the families of Palestinians in Israeli prisons, including those held for violent attacks, but, unlike Hamas, recognizes Israel’s right to exist and has to an extent coordinated with Israeli security forces.

Mr. Biden and Mr. Netanyahu are at odds over the day-after question. While Mr. Biden agrees that Hamas must be removed from power in Gaza, he opposes an Israeli re-occupation of the coastal enclave. Instead, he favors what he calls a “revitalized” Palestinian Authority taking over Gaza as well. But Mr. Netanyahu has resisted that and on Tuesday said only Israel can ensure that Gaza will remain demilitarized after Hamas is destroyed. “I’m not ready to close my eyes and accept any other arrangement,” he said.

For all their differences, Biden administration officials argue that the president’s strategy has paid dividends. By keeping Israel close, they said, he has helped prevent Israel from widening the war by going after Hezbollah in Lebanon; forced Israel to reopen Gaza to humanitarian aid after initially vowing to block any food, water and other supplies; encouraged the now-expired pause in fighting that enabled the release of more than 100 hostages; and prompted Israel to take more steps to curtail civilian casualties.

As Israeli forces push into southern Gaza, they have published maps of safe zones where civilians can shelter from the fighting and, according to U.S. officials, sought to calibrate their targeting to avoid as many mass casualty attacks. Nonetheless, the Gaza Health Ministry has reported that hundreds have been killed just in the last few days, and critics have scorned the maps as ineffective in an area with so little mass communication. Speaking privately, Biden administration officials acknowledge the Israelis have not done as much as Washington would like to spare civilians but said they have gotten the message and are trying.

“Israel has heard from us loud and clear our expectation that they uphold international humanitarian law, abide by the rules of war, and take steps to minimize, to every extent possible, civilian casualties as they persecute this war against Hamas,” Olivia Dalton, a White House spokeswoman, told reporters on Air Force One on Tuesday as Mr. Biden traveled to Boston.

While the war continues, the clock is ticking and White House officials recognize that there may be a limit to how long they can preserve the public alignment with Israel.

“I think U.S. policy has a shelf life of four to six weeks,” said Cliff Kupchan, chairman of the Eurasia Group, who had just returned from a trip to the region. “If this war is still ongoing in January, dissent within the Democratic Party and strong international pressure will probably cause Biden to pressure Israel to scale back military operations.”