Not long after Russia invaded Ukraine, the Democratic Socialists of America released a statement that drew instant reproof.

The group condemned the invasion, but also urged the United States “to withdraw from NATO and to end the imperialist expansionism that set the stage for this conflict.”

The position — a watered-down version of a prior, even more pointed statement from the group’s international committee — drew rebukes from a White House spokesman and from a number of Democratic candidates and elected officials, from Long Island congressional contenders to officials in New Jersey and Pennsylvania. But in the New York City area, where the D.S.A.’s largest chapter wields substantial influence, it has also created a challenging dynamic for politicians aligned with the organization.

In the state’s 16th Congressional District, a refugee from Kosovo is making foreign policy central to his primary challenge of Representative Jamaal Bowman, a former middle school principal from Yonkers who rose to power with support from the Democratic Socialists of America.

In New York City, Democratic congressional candidates are debating America’s role in the world. And even before D.S.A.’s most recent statement, City Council members were clashing over the history of American and NATO intervention.

With a majority of Americans backing Ukraine as it struggles to repel a bloody, often live-streamed Russian invasion, the D.S.A.’s desire for a policy discussion about NATO appears to have sown unease in campaign circles: None of the nine New York City candidates the D.S.A. endorsed this year would consent to an interview on the topic, even as more centrist Democrats are now using the subject as a cudgel.

“We’re refugees from Kosovo, a country where me and my family had to flee because of ethnic cleansing and were saved, frankly, by U.S. and NATO intervention there,” Vedat Gashi, a Democrat challenging Mr. Bowman, said last week. “Blaming Ukraine and NATO for the escalation of this Russian invasion of Ukraine is to me, at the very best case, naïve and certainly wrong.”

The D.S.A. argues that NATO promotes a militarized response to conflict at the expense of diplomacy, and that economic sanctions too often victimize working people. In the case of Ukraine, many D.S.A. members say that the United States, by encouraging the expansion of NATO eastward, provoked Russia.

“There is a longstanding tradition with the U.S. left as well as in Europe that NATO has played a role, especially since the collapse of the Soviet Union, in emphasizing militarized solutions when diplomacy could lead to more long-term stability,” said Ashik Saddique, a member of the D.S.A.’s National Political Committee. “It feels a little bit absurd for people to be acting like it’s a political crime to criticize NATO.”

Mr. Gashi called on Mr. Bowman to fully disavow the D.S.A. stance.

Mr. Bowman has chosen a subtler tack, signaling distance from the D.S.A.’s position, without the sort of direct condemnation that might alienate a component of his base and play into his opponent’s hands. He declined to comment for this article, but in a prior statement, he said he supports NATO, “and will continue to do so during this crisis.”

Mr. Bowman’s district includes a sizable population of Ukrainian immigrants, and last week, he called more than a dozen who have written him letters, his office said. He has also joined the Congressional Ukraine Caucus and has put together a bipartisan letter asking President Biden to let at-risk Ukrainians enter the country without visas.

But Ukrainians are not the only constituents D.S.A.-aligned politicians need to consider amid the crisis, said Drisana Hughes, the former campaign manager for India Walton, the D.S.A.-backed candidate for mayor of Buffalo, and a campaign strategist at Stu Loeser and Co.

“I don’t think it’s just Ukrainian constituents; I think it’s Polish constituents, Finnish constituents,” Ms. Hughes said. “It’s a lot of countries that are sensitive to Russian aggression and anyone concerned about the future of Europe in particular.”

Certainly, whatever the balancing act for some Democrats, tensions are clearly evident for Republicans. Even as many express solidarity with Ukraine, former President Donald J. Trump has lavished praise on Russian President Vladimir V. Putin — just a few years after Mr. Trump’s first impeachment centered on issues including pressuring Ukraine for political favors. The only people to vote against a recent House resolution in support of Ukraine were three Republican members of Congress. And some right-wing media figures, like Fox News host Tucker Carlson, have until very recently sounded protective of Mr. Putin.

Still, in New York, the rifts around the Russian invasion have taken on more urgency on the Democratic side, including in the battle for New York’s 11th Congressional District, which was recently redrawn to take in both Staten Island to Park Slope, and where the two most prominent Democratic contenders are military veterans.

Brittany Ramos DeBarros, a member of D.S.A., has endorsed working “with international partners to supply and support civil-military defense tactics,” and said “no” when asked directly in an interview if the U.S. should withdraw from NATO. But in 2019, she was listed as a speaker at an anti-NATO event, and acknowledged that she “attended a meeting about that” in her days as an anti-war activist. Her campaign said that she does not support withdrawing from NATO “at this time.”

“‘Not at this time’ means that right now is the time to save lives, and to de-escalate the situation,” she said in an interview. “If people would like to have a broader conversation about understanding how we got here and diagnosing what we need to do in order to, you know, shape a different future, then that can come once we have removed ourselves from the brink.”

Her campaign has noted that her main Democratic primary opponent, former Representative Max Rose, initially voiced skepticism of the first impeachment proceedings against Mr. Trump.

Mr. Rose, seen by party strategists as the likely front-runner, did vote to impeach Mr. Trump and said he took the subject “very seriously. But I did not blink in the face of holding Donald Trump accountable for his egregious actions.”

He also condemned the D.S.A.’s position regarding NATO and called for building “an even stronger NATO alliance.”

“America’s unilateral withdrawal from NATO is perhaps the most harmful, stupidest thing, foreign policy decision, that we could be considering right now,” he said. “America has to double down on its alliances, particularly its trans-Atlantic ones.”

Some left-wing candidates also directly rejected the D.S.A. statement.

“I don’t agree with the D.S.A.’s stance on the U.S. exiting NATO,” said Rana Abdelhamid, a member of D.S.A. who is challenging Representative Carolyn Maloney in a New York City district that, under redistricting lines, has shed some left-wing neighborhoods. “NATO is one of the primary lines of defense that we have to address Russian aggression towards Ukraine.”

But many other New York City officials aligned with D.S.A. — some of whom have weighed in often on other national and international issues in the past — were far more circumspect.

“Thanks for reaching out, but our campaign has no comment on that,” emailed Stephen Wood, a spokesman for Brooklyn State Senate candidate David Alexis, on Wednesday.

Other elected officials who declined to comment or did not return requests for comment included Representative Alexandria Ocasio-Cortez; State senators Julia Salazar and Jabari Brisport; and Assembly members Zohran Kwame Mamdani, Marcela Mitaynes and Phara Souffrant Forrest. Nor did Assemblywoman Emily Gallagher, of Brooklyn, agree to comment.

“If you’d like to write about all electric buildings act, LLC disclosure legislation, or any of my other work as a legislator I’d be happy to talk,” Ms. Gallagher said.

Locally, the D.S.A.’s viewpoint has been most energetically advanced by Kristin Richardson Jordan, a councilwoman from Harlem and a democratic socialist, who was not backed by the organization in her campaign for office.

“In 2014, the U.S. helped overthrow Ukraine’s democratically elected leader in an illegal coup, helped install a fascist government and empowered a far right military all with the goal of destabilizing Russia,” Ms. Jordan said recently on Twitter, accusing the United States and European Union of “provoking Russia with NATO expansion” — comments that some said provided cover for Mr. Putin.

She did not respond to requests for comment. But during a recent radio appearance, Ms. Jordan was asked to justify her position. She repeated her prior claims, and drew open pushback from Council colleagues.

“I’m not sure it makes sense to dive into the details of international politics when I’m in local government,” she said on The Brian Lehrer Show.

In Yonkers, where Mr. Bowman and Mr. Gashi are running, Kiril Angelov, the pastor at St. Michael the Archangel Ukrainian Catholic Church, said he had seen both men at a recent service.

“I hope that every single politician is seeing the situation in Ukraine with open eyes and with open hearts,” he added.