Prime Minister Benjamin Netanyahu of Israel took much personal credit this weekend for an emerging plan to free all remaining hostages from Hamas and end the two-year war in Gaza.

But it was abundantly clear to Israelis, and to Palestinians and others in the region, that the one calling the shots was President Trump.

Mr. Netanyahu asserted in a brief, televised address to the nation on Saturday that the plan was the result of a diplomatic move that he had coordinated over weeks, and jointly presented, with Mr. Trump and his team.

Mr. Trump told it a bit differently. In a conversation on Saturday with a leading Israeli correspondent for Axios and for Israel’s most popular news channel, the president suggested that he had strong-armed a somewhat reluctant Mr. Netanyahu into accepting the terms.

“I said, ‘Bibi, this is your chance for victory,’ Mr. Trump related, referring to Mr. Netanyahu by his nickname. “He was fine with it,” Mr. Trump continued, adding, “He’s got to be fine with it. He has no choice. With me, you got to be fine.”

Mr. Netanyahu is in no position to defy Mr. Trump while facing international censure over Israel’s conduct in the war and growing international isolation, analysts say, increasing its reliance on the United States.

“Trump doesn’t threaten Netanyahu; he orders him,” wrote Nahum Barnea, a prominent Israeli political columnist, in Sunday’s Yedioth Ahronoth, a mainstream Hebrew daily, in an article with the headline “He’s the Boss.”

The turn of events in recent days “clearly illustrated that state of affairs to everyone,” Mr. Barnea continued, referring to Mr. Trump’s ultimatum to Hamas on Friday to accept the proposal, followed hours later by the president’s interpretation of a highly qualified acceptance by the militant group as an unqualified yes.

Israelis then learned from Mr. Trump, via a social media post on Saturday, that Israel had already agreed to an initial withdrawal line within Gaza for the first phase of the deal, which proposes exchanging about 20 living hostages and the bodies of about 28 believed to be dead for 250 Palestinian prisoners serving life terms and hundreds more Gazans detained during the war.

Once Hamas signs on, Mr. Trump announced in the same post, a cease-fire would “IMMEDIATELY” go into effect.

For months Mr. Netanyahu has been engaged in a delicate balancing act. He has been determined to fulfill his pledge of total victory over Hamas, whose attack on Israel on Oct. 7, 2023, ignited the war, and to ensure his own political survival by appeasing his far-right coalition partners who oppose any deal that leaves Hamas standing.

At the same time, the humanitarian crisis in Gaza, where tens of thousands of Palestinians have been killed and hunger has run rampant, has stirred global wrath. Polls have shown that a majority of Israelis, long skeptical of the chances of a “total victory,” favor ending the war in order to get the hostages back. And Mr. Trump’s patience appears to have worn thin.

“It doesn’t look like Hamas is leaving, and it doesn’t look like the total victory he promised,” Mitchell Barak, an Israeli pollster who worked as an aide to Mr. Netanyahu in the 1990s, said of the prime minister. “I think he realized his credit with Trump ran out.”

Unlike the defiant stance Mr. Netanyahu often took against the Biden administration or President Barack Obama, Mr. Barak said: “For first time Netanyahu cannot disregard the wishes of an American president, because of the way Trump operates. Trump is unpredictable and will not fall in line with the Israeli position.”

That has become more evident in recent days as Mr. Trump has weighed his relations with Mr. Netanyahu against his interests and ties with other countries in the region, including Turkey, whose leader, President Recep Tayyip Erdogan, has used harsh rhetoric against Israel, and Qatar, a country that Mr. Netanyahu recently accused of harboring terrorists.

Only two months ago, Mr. Netanyahu’s government approved a plan to expand the war by taking control of Gaza City, a risky decision that went against the recommendations of the Israeli military. Israeli leaders described the city as one of Hamas’s last bastions and presented the operation as an essential step toward wiping out the group’s military and governing capabilities.

The military advance has been slow and largely focused on forcing most of the roughly one million residents to move south.

Mr. Netanyahu on Saturday credited both the military and diplomatic pressure with pushing Hamas into acceptance.

But with none of the technical details settled for the release of hostages, with talks set to start in Egypt on Monday, Mr. Trump had already essentially halted the advance on Gaza City.

“Israel must immediately stop the bombing of Gaza, so that we can get the Hostages out safely and quickly!” Mr. Trump wrote on social media on Friday, after receiving Hamas’s response.

By Saturday, the Israeli military was limiting its actions to what Israeli officials called defensive operations and responding to immediate threats, undercutting Mr. Netanyahu’s long-held position that negotiations would take place only under fire.

Mr. Netanyahu also boasted on Saturday that Israel was “on the verge of a very great achievement” of getting its hostages back even as its forces remained in “all the controlling areas deep inside” the Palestinian enclave.

The map of the initial redeployment line presented by Mr. Trump did show Israel’s maintaining its hold over large swaths of territory within Gaza’s borders, but it also indicated that the troops would evacuate a key corridor bisecting the enclave and cutting off the north from the south.

Less than a week ago, Mr. Netanyahu’s defense minister, Israel Katz, announced that the troops were in the process of “completing the takeover” of the Netzarim Corridor, which the military had already seized and evacuated in the past.

Mr. Trump humiliated Mr. Netanyahu in the eyes of many Israelis by putting him on the phone to the prime minister of Qatar, Sheikh Mohammed bin Abdulrahman al-Thani, to apologize for Israel’s botched attempt last month to kill Hamas leaders in the Qatari capital, Doha. The White House issued a photograph of Mr. Netanyahu reading his written apology into the receiver as Mr. Trump propped the phone on his lap.

In addition, Mr. Trump and his team compelled Mr. Netanyahu to sign onto a clause in the deal promising, however vaguely and subject to conditions, a “credible pathway” to Palestinian statehood, when one of his main calling cards has been the prevention of a Palestinian state.

“His entire career has been in a free fall in the last few days,” Mr. Barak said, adding, “He agreed to everything.”

Still, other experts note that as Israel’s longest serving prime minister, Mr. Netanyahu has survived many a knock to his image in the past.

“Bibi has the ability to know what the other side wants and needs,” said Mazal Mualem, an Israeli political commentator for Al-Monitor, a Middle East news site, and the author of a biography of the Israeli leader. “He knows when to show restraint.”

So far, Ms. Mualem said, Mr. Netanyahu appears to have convinced his party and his political base that the deal is a win for Israel and is owning it.

And Mr. Netanyahu, who looks at things through the lens of history, she added, knows that “to get into a fight with Trump will hurt Netanyahu, not Trump.”