Few issues have been more divisive among the Republican presidential candidates than the war in Ukraine and how, if at all, the United States should be involved.

It has illuminated one of the biggest ideological divides within the Republican Party: between traditional members who see the United States as having a significant role to play in world affairs, and an anti-interventionist wing that sees foreign involvement as a distraction from more important issues at home.

The old school has more adherents in the 2024 field, including Nikki Haley, Mike Pence and Tim Scott, who support sending Ukraine military equipment and weapons but not troops. This aligns with President Biden’s strategy, though they maintain that Mr. Biden is executing it wrong.

But the anti-interventionist wing is dominant in terms of influence, with two members, Donald J. Trump and Ron DeSantis, far outpolling everybody else.

Only one candidate, Will Hurd, wants to significantly expand U.S. involvement.

The anti-interventionists

Donald J. Trump

Former President Donald J. Trump has said that the war in Ukraine is not of vital importance to the United States.

In a CNN town hall event, he did not give a straight answer when asked repeatedly whether he would continue to provide military aid, instead declaring that he would end the war “within 24 hours” by meeting with Presidents Vladimir V. Putin of Russia and Volodymyr Zelensky of Ukraine. He claimed falsely that the United States was sending so much equipment that “we don’t have ammunition for ourselves.”

Mr. Trump — who was impeached in 2019 for withholding aid to Ukraine to pressure Mr. Zelensky to help him electorally — also suggested to Fox News that he could have prevented the war by ceding Ukrainian land to Russia. “I could’ve made a deal to take over something,” he said. “There are certain areas that are Russian-speaking areas, frankly.”

Ron DeSantis

Gov. Ron DeSantis of Florida has called the war a “territorial dispute” whose outcome does not materially affect the United States.

“While the U.S. has many vital national interests — securing our borders, addressing the crisis of readiness with our military, achieving energy security and independence, and checking the economic, cultural and military power of the Chinese Communist Party — becoming further entangled in a territorial dispute between Ukraine and Russia is not one of them,” he told the Fox News host Tucker Carlson in March.

After criticism from fellow Republicans, he backtracked, saying that his comments had been “mischaracterized” and that Russia’s invasion was wrong.

He has since endorsed a cease-fire, saying he wants to avoid a situation “where you just have mass casualties, mass expense and end up with a stalemate.” He has maintained his position that the United States should not get more involved.

Vivek Ramaswamy

The entrepreneur Vivek Ramaswamy opposes aid to Ukraine because, he argues, the war does not affect American interests.

He says he would pursue an agreement that would offer sweeping concessions to Mr. Putin, including ceding most of Ukraine’s Donbas region to Russia, lifting sanctions, closing all U.S. military bases in Eastern Europe and barring Ukraine from NATO. In exchange, he would require Russia to end its military alliance with China and rejoin the START nuclear treaty.

“I don’t think it is preferable for Russia to be able to invade a sovereign country that is its neighbor, but I think the job of the U.S. president is to look after American interests, and what I think the No. 1 threat to the U.S. military is right now, our top military threat, is the Sino-Russian alliance,” Mr. Ramaswamy told ABC News. “I think that by fighting further in Russia, by further arming Ukraine, we are driving Russia into China’s hands.”

The traditionalists

Nikki Haley

Nikki Haley, a former ambassador to the United Nations, says that it is “in the best interest of America” for Ukraine to repel Russia’s invasion, and that she would continue sending equipment and ammunition.

“A win for Ukraine is a win for all of us, because tyrants tell us exactly what they’re going to do,” she said on CNN. She added: “China says Taiwan’s next — we’d better believe them. Russia said Poland and the Baltics are next — if that happens, we’re looking at a world war. This is about preventing war.”

Victory for Ukraine, Ms. Haley said, would “send a message” more broadly: warning China against invading Taiwan, Iran against building a nuclear bomb, and North Korea against testing more ballistic missiles. To Russia, it would signal that “it’s over.”

In a speech at the American Enterprise Institute, she said President Biden had been “far too slow and weak in helping Ukraine.”

Mike Pence

Former Vice President Mike Pence supports aid to Ukraine and has accused Mr. Biden of not supplying it quickly enough. In June, he was the first Republican candidate to travel to Ukraine, where he met with Mr. Zelensky.

Like Ms. Haley, he has described helping Ukraine as a way to show China that “the United States and the West will not tolerate the use of military force to redraw international lines,” a reference to a possible Chinese invasion of Taiwan.

This position sets him apart from the president he served under. Criticizing Mr. Trump’s description of Mr. Putin as a “genius,” Mr. Pence said on CNN that he knew “the difference between a genius and a war criminal.”

He has emphasized that he would “never” send American troops to Ukraine, and said he did not yet want to admit Ukraine to NATO because he wanted to prevent the United States from becoming obligated to send troops. But he said he was open to admitting the country into NATO after the war.

Tim Scott

Senator Tim Scott of South Carolina supports aid to Ukraine and told NBC News that Mr. Biden had “done a terrible job explaining and articulating to the American people” what the United States’ interests are there, an argument Mr. Pence has also made.

“First, it prevents or reduces attacks on the homeland,” Mr. Scott said. “Second, as part of NATO and land being contiguous to Ukraine, it will reduce the likelihood that Russia will have the weaponry or the will to attack on NATO territory, which would get us involved.”

He has endorsed a forceful defense of Ukraine from the start, writing in March 2022 that the fight was “for the principles that America has always championed.” That May, he voted for an emergency funding measure that went beyond what Mr. Biden proposed. He accused Mr. Biden of waiting “too long to provide too little support,” but Mr. Biden supported the increase.

Chris Christie

Former Gov. Chris Christie of New Jersey has said that the United States should continue to support Ukraine until the war is “resolved.”

“None of us like the idea that there’s a war going on and that we’re supporting it, but the alternative is for the Chinese to take over, the Russians, the Iranians and the North Koreans,” Mr. Christie said in a CNN town hall, calling the conflict “a proxy war with China.”

He added that “some kind of compromise” with Russia might eventually be needed, and that the United States should help negotiate it once “Ukraine can protect the land that’s been taken by Russia in this latest incursion.”

He has said that Mr. Trump “set the groundwork” for the war and called him “Putin’s puppet.” And he compared Mr. DeSantis to Neville Chamberlain, the British prime minister who tried to appease Hitler.

Asa Hutchinson

Former Gov. Asa Hutchinson of Arkansas supports aid to Ukraine with audits to ensure funds are used as intended. He told C-SPAN that U.S. leadership was “important in supporting Ukraine and bringing the European allies together” against Russia, and that he disagreed with Mr. Trump’s and Mr. DeSantis’s more “isolationist view.”

Like several other candidates, he has argued that allowing Russia to win would embolden it and other authoritarian countries to attack elsewhere.

“If we stand by and let this nation falter, it leaves a hostile Russia on the doorstep of our NATO allies,” he said, adding, “By taking a supportive and public stand in Ukraine, we’re sending a message to Russia and to China that their aggressive posture towards other nation-states is unacceptable.”

Doug Burgum

Gov. Doug Burgum of North Dakota has indicated that he supports military aid with “accountability on every dollar.”

“Russia cannot have a win coming out of this, because if it’s a win for them, it’s a win for China,” Mr. Burgum told KFYR, a television station in North Dakota, while adding that he wanted Europe to shoulder more of the financial burden.

He told CNN in June that the domestic turmoil in Russia had created an opening that the United States and NATO could exploit. “Let’s give them the support they need,” he said of Ukraine, without elaborating. “Let’s get this war over now instead of having it be protracted.”

Francis Suarez

Mayor Francis X. Suarez of Miami supports aid but wants to tie it to new NATO rules requiring Europe to carry an equal burden.

In a National Review essay, he said Mayor Vitali Klitschko of Kyiv had warned him that if Mr. Putin was not stopped, Russia and China would continue to attack the West, possibly including the United States. Mr. Suarez added that Russia had to be defeated because it was part of “a broader resurgence of communist-inspired regimes,” though Mr. Putin’s Russia is not communist.

Without naming him, Mr. Suarez criticized Mr. DeSantis’s position. “It doesn’t take a Harvard lawyer to see that the war in Ukraine is not a territorial dispute,” he wrote, shortly after Mr. DeSantis used that phrase to describe it. “It is a moral and geopolitical struggle between two visions of the world.”

The hawk

Will Hurd

Former Representative Will Hurd of Texas — who said from the start that the United States should send Ukraine “as much weaponry as we can” — has espoused a more hawkish policy than any other major candidate, arguing that the United States should go well beyond providing equipment and weapons.

Mr. Hurd told ABC News that he supported establishing and helping enforce a no-fly zone over Ukraine. NATO leaders and U.S. lawmakers from both parties rejected that last year, saying they feared escalation. Mr. Hurd has brushed that concern aside, arguing that Mr. Putin had not escalated when a mercenary leader threatened a coup.

He said that the United States should help Ukraine retake not only the territory Russia invaded in 2022, but also Crimea, which Russia annexed in 2014.