Representative Alexandria Ocasio-Cortez is one of the most powerful progressive leaders in the country, a politician most liberal Democrats want on their side — in person and on Twitter.

But short of that, no Democratic candidate running for mayor of New York City wants to alienate her. Last week, Andrew Yang learned that the hard way.

After the mayoral candidate laid out his plan to support a “Green New Deal for public housing,” he drew a near-instant rebuke from Ms. Ocasio-Cortez over the details.

“I wrote the original Green New Deal for Public Housing,” she wrote on Twitter last Friday. “This isn’t that plan.”

Mr. Yang quickly reached out to the congresswoman, speaking to her that same day, according to allies who heard about the conversation.

The interaction was a vivid illustration of Ms. Ocasio-Cortez’s extraordinary influence on New York’s political landscape as another election unfolds.

With less than five months before the Democratic primary election, the questions of how and whether Ms. Ocasio-Cortez, 31, will use her platform to shape the New York City mayor’s race are sources of great speculation — and angst — in pockets of her hometown.

An endorsement from Ms. Ocasio-Cortez, who represents parts of the Bronx and Queens, could affirm the recipient as the liberal standard-bearer in the contest or elevate a lesser-known contender and signal a new measure of viability around their campaign.

Certainly, endorsements alone rarely determine the outcome of campaigns, and Ms. Ocasio-Cortez’s are no different. Indeed, her endorsees have a mixed record of success both in New York and nationally. But because she commands attention and resonates with the city’s left wing in ways that no mayoral candidate can claim on their own, her blessing would almost certainly have outsize impact on the muddled field.

“If you’re looking to sew up the left, I’m sure you’re looking for A.O.C.’s endorsement,” said Donovan Richards, the Queens borough president.

With registered Democrats far outnumbering registered Republicans, the June 22 Democratic primary is likely to determine the city’s next mayor. Despite that compressed time frame, a number of strategists and other top potential endorsers appear to be holding their fire at least until there is more clarity around which candidates have staying power. Ms. Ocasio-Cortez could make a similar calculation.

“My observation is, it seems that she would make an endorsement when a candidate really lines up with her values and she feels like she could make a big difference,” said Susan Kang, a political science professor at the John Jay College of Criminal Justice who is a steering committee member of the New York City Democratic Socialists. “The mayoral race is a little bit of a black box.”

Interviews with more than a dozen elected officials, party leaders, activists and strategists across the city suggest that there is little expectation that Ms. Ocasio-Cortez will endorse in the mayor’s race anytime soon — if she does so at all.

Ms. Ocasio-Cortez has been intensely focused on a range of federal priorities, from pressing for additional Covid relief to confronting the aftermath of the pro-Trump insurrection at the Capitol. But she suggested on Tuesday that the mayoral race, as well as other New York City contests including City Council races, was “absolutely of really important interest.”

“It’s definitely something that I’m paying close attention to,” she said Tuesday night, after holding a virtual town hall meeting. “And of course, we want to make sure that we are also being very receptive to our community in this process.”

Ms. Ocasio-Cortez was elected in 2018 after defeating Joseph Crowley, then the No. 4 House Democrat, in a shock primary upset. Since then, she has endorsed, sometimes late, in a number of high-profile New York races — though she does not jump into every contest.

When she has weighed in, her choices have often been closely aligned with those of institutional allies like the Working Families Party and the Democratic Socialists of America, and neither group has endorsed in the mayor’s race.

“I don’t see her getting involved,” said State Senator Jabari Brisport of Brooklyn, saying that he appreciated her work in Congress. “I haven’t heard anything from her being interested in doing that.”

Mr. Brisport, who like Ms. Ocasio-Cortez has been embraced by the D.S.A., said he was primarily focused on City Council races at this point, which is also where a number of prominent liberal leaders and groups have put their emphasis.

The speculation around Ms. Ocasio-Cortez’s intentions generally falls into three buckets: She could stay out of the race entirely, endorse Scott M. Stringer, the city comptroller, or support a woman of color.

Other scenarios could also materialize.

There is the possibility that Ms. Ocasio-Cortez won’t endorse at all, but will weigh in on the race periodically as a way to elevate her key policy priorities. Some of her allies, for instance, hope that she uses the race to draw attention to her own proposal for a Green New Deal for Public Housing, the measure she raised on Twitter with Mr. Yang.

Asked whether she planned to endorse in the mayoral race and how she intended to use her influence, Ms. Ocasio-Cortez said that she did not have “any concrete answers” at the moment, but emphasized her broader priorities around making the city more equitable.

“Addressing inequality — and not just economic inequality — health inequality, criminal justice inequality, and so, you know, these are issues that are a major priority for me and for our community,” she said.

Mr. Stringer, for his part, has pulled in endorsements from a number of prominent progressive lawmakers, several of whom are seen as aligned closely with Ms. Ocasio-Cortez. But he is also a white man who has worked in politics for decades, at a moment when some left-leaning voters would prefer to elevate a person of color.

Maya Wiley, a former top counsel to Mayor Bill de Blasio, and Dianne Morales, a former nonprofit executive, are both progressive women of color who are active on the virtual campaign trail. But whether they can demonstrate real traction in the race remains unknown. Ms. Wiley, who in a recent poll came in at 8 percent, has qualified for matching funds from the city; Ms. Morales, who in that poll was at 2 percent, has said that she expects to hit the key fund-raising threshold for the next filing period.

Carlos Menchaca, a Brooklyn city councilman, is deeply progressive, but has struggled to get off the ground.

Then there is Mr. Yang, who has fashioned himself as the anti-poverty candidate. That message could appeal to progressives, but he also faces skepticism from the left over issues including policing and education. Ms. Wiley has sharply questioned Mr. Yang around reporting concerning a challenging culture for women working on his presidential campaign, and Ms. Ocasio-Cortez has been a vocal critic of sexism in the workplace.

Assemblyman Ron T. Kim, who was endorsed by Ms. Ocasio-Cortez last year and is now a prominent supporter of Mr. Yang’s mayoral bid, said that he was encouraged when he heard that Mr. Yang had engaged directly with Ms. Ocasio-Cortez. He said he was hopeful that the congresswoman and Mr. Yang could connect on policy matters including the environment and housing and other anti-poverty measures.

“If there is an alignment, I think it would be such a powerful combination of electeds,” said Mr. Kim, asked about the prospect of an Ocasio-Cortez endorsement for Mr. Yang.

Representatives for Mr. Yang and Ms. Ocasio-Cortez declined to comment on their conversation.

Jumaane D. Williams, the New York City public advocate and a coveted endorser himself, said that if Ms. Ocasio-Cortez decides to weigh in, “that would be an awesome indicator endorsement.” But no endorsement or potential endorsement alone, he stressed, is decisive.

“The question is, do you have the infrastructure to have it translate to more on the ground, and then into votes,” he said.