President Trump’s grip on the Republican Party remains indisputable, according to the latest New York Times/Siena poll, with a majority of Republicans and Republican-leaning independents wanting to see the next presidential nominee follow his lead on most issues.

But there are signs that some in the G.O.P. coalition are looking to move beyond the Trump era. Thirty-seven percent want to see the party’s next nominee move in a different direction, including a majority of Republican-leaning independents. And divisions are emerging even among the president’s strongest supporters when it comes to questions about the economy and foreign policy, as the war with Iran has driven up gas prices.

Mr. Trump remains overwhelmingly popular among the party faithful. Three-quarters of Republicans and Republican-leaning independent voters approve of his job performance, the poll found, even as the president’s approval rating among the wider American electorate has fallen to a second-term low of 37 percent.

The president’s popularity within his party has helped him oust several Republican elected officials who have crossed him by supporting challengers in party primaries in Louisiana and Indiana. And it has given him the clout to persuade several Republican-led states to draw new House maps that will be more favorable to the party.

But in a general election where Democrats and independents who lean toward Democrats will also vote — often at higher rates than Republicans — the dissatisfaction illustrated by Mr. Trump’s sagging approval ratings and the unpopularity of the war could still cost Republicans the control of Congress.

Still, growing disapproval among the wider electorate has barely dented Mr. Trump’s standing among Republican supporters, pointing to the entrenched polarization in American politics.

Nearly 70 percent of Republican supporters say they approve of how Mr. Trump has handled the economy, even as the poll found that 55 percent have a negative view of current economic conditions, a 9-percentage-point jump since a January Times/Siena poll. And disapproval over how the president has handled the cost of living has climbed to 40 percent, up from 26 percent in January. Gas prices and inflation have risen sharply since Mr. Trump took the nation to war with Iran in February.

Though Republicans remain largely unified, nothing has divided them more than the president’s aggressive foreign policy.

Forty-five percent of Republican supporters now say it is best for the United States to be active in world affairs to maintain security and prosperity, while half say that they want the country to “pay less attention to problems overseas.” That was a significant shift from 2023, when a large majority of Republicans called for focusing on problems at home.

The change suggested that many Republicans were following the lead of Mr. Trump, who campaigned against foreign wars but has used his second term to go to war with Iran and to deploy the military to install a new leader in Venezuela.

David Blanch, a retired real estate investor in Pasadena, Md., said that he strongly supported Mr. Trump taking military action after a number of his predecessors had worried about Iran’s nuclear capabilities but not “done a damn thing about it.”

“They cannot have a nuclear weapon,” said Mr. Blanch, 88, who voted for Mr. Trump every time he ran for president. “That nuclear weapon scares the hell out of me, frankly.”

In some areas, though, Republicans seem to be diverging from Mr. Trump on foreign policy. While Mr. Trump often rails against NATO and has threatened several times to leave it, more than half of Republicans and Republican-leaning independents support keeping the United States in the alliance.

The divisions on foreign policy suggest that there are different paths open to Republicans weighing runs for president in 2028, including Secretary of State Marco Rubio, who is seen as more interventionist, and Vice President JD Vance, who is seen as more isolationist.

There is a divide among Republican backers depending on how closely tethered they feel to the party. Fifty-five percent of independents who say they lean toward the Republican Party want the party to move on from Mr. Trump, while nearly two-thirds of those who identify fully as Republicans want it to follow his lead. Leaners, as they are sometimes known, are less reliable party voters, but they play key roles in elections.

The survey revealed rapidly changing views toward Israel, an increasingly divisive issue for Republicans.

While a majority of Republicans and Republican leaners still support providing economic and military aid to Israel, 37 percent now oppose such assistance, up from 28 percent in September. Twenty-nine percent say Mr. Trump is too supportive of Israel, with young Republicans more than three times as likely as those over age 45 to say that.

Stanley Hicks, a 22-year-old student at Western Michigan University, said he had initially backed Mr. Trump on Israel as it responded to the Hamas-led attack on Oct. 7, 2023.

“I was like, perfect, yep, help them a little bit,” said Mr. Hicks, who voted for Mr. Trump in 2024. “They’re a really strong ally of ours.”

But he said he changed his mind as the conflict dragged on and the White House did not tell Israel, “‘You’re going too far.’”

Sixty-two percent of Republican supporters say that going to war was the right decision, and more than two-thirds say they expect the war to be successful at eliminating Iran’s nuclear program.

At the same time, only 43 percent think the Iran war has been worth the costs, and 30 percent think the war was the wrong decision.

“Unfortunately, now we’re fighting a war that, to be honest, I have no idea why we’re there,” said Nathan Coletti, 49, who voted for Mr. Trump in 2024. “And I would tell you that I am actually embarrassed that I voted for him.”

Mr. Coletti, who works as a wastewater operator in Rock Springs, Wyo., said he wants the president to spend less on the war and focus more on economic concerns at home.

“If your family is starving, you have no right in trying to feed another family if your family is dying,” he said. “And that’s exactly how I feel.”

The vast majority of Republican supporters, 72 percent, say that Mr. Trump has been about right in his use of military force, while 19 percent say he has been too willing to use it. But when asked more generally about when it is justified to use force, they were more divided. A slim majority say it is not justified unless the hostile government poses an immediate threat. Thirty-eight percent say it is justified to use military force even if there is no threat.

One area of domestic policy where the president’s support appears solid is immigration, with 80 percent of Republican supporters approving of his job performance and 77 percent hoping for his successor to follow his lead.

When it comes to the economy, 31 percent of all Republicans, including 47 percent of young Republicans, say they want to move the party’s policies in a different direction on tariffs, one of Mr. Trump’s signature policies.

And a majority of Republicans say they would prefer a candidate who promises to cut corporate taxes to one who calls for imposing tariffs, a shift from a 2023 Times/Siena poll that found Republican voters more split between the two approaches.

The demeanor of Mr. Trump, who recently got into a public dispute with Pope Leo XIV, is increasingly concerning some members of his party. More than 20 percent say they have been offended by something Mr. Trump said recently, up from 13 percent in 2024.

Tucker Carlson, who has emerged as one of the most prominent conservative critics of Mr. Trump, is viewed favorably by 37 percent of Republicans and unfavorably by 29 percent. The podcaster Joe Rogan, who endorsed Mr. Trump in 2024 but has since criticized him at times, is viewed favorably by 54 percent of Republicans. And for all the attention that white nationalist Nick Fuentes attracts online, 69 percent of Republicans say they have not heard of him.

At the same time, more Republicans are expressing concern about the changing racial and ethnic composition of the country. One-quarter of Republicans now say it is a bad thing that white people are declining as a share of the U.S. population, up from 16 percent in 2023.

There is little doubt that most Republicans will remain loyal to their party at the ballot box. The poll found that 88 percent of them plan to vote for Republicans in the fall.

Mary Spradlin, 65, who owns a small business in Liberty Hill, Texas, said she was hoping for Republican victories that would continue to allow Mr. Trump freedom to pursue his agenda.

“I believe that he truly wants the best for America. I believe he is not in it for himself like most of our politicians,” she said. “I’m hoping that we can boot out some of the Democrats and take over even with a bigger majority with the Republicans.”