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The race for mayor in New York City took an unusual and turbulent turn on Monday as some Democrats lined up to suggest ways to defeat Zohran Mamdani, the one candidate officially running on their party’s line.

Former Gov. Andrew M. Cuomo and Mayor Eric Adams, two Democrats currently planning to run in the November election as independents, each called on the other to drop out.

A third independent candidate, Jim Walden, was less specific in his similarly themed proposal last week. He suggested that a poll be taken in the fall to determine who among what he referred to as the four “free-market candidates” has the best chance of defeating Mr. Mamdani in a race that “pits capitalism against socialism.” Mr. Mamdani’s left-leaning platform and democratic socialist affiliation have alarmed some of the Democratic establishment.

Whoever doesn’t win the poll, Mr. Walden said, should pledge to bow out and support the winner.

Mr. Walden’s proposal was backed on Monday by Mr. Cuomo as well as former Gov. David A. Paterson, a Democrat who held a news conference to announce his support alongside the Republican billionaire John Catsimatidis and Sid Rosenberg, a radio host and supporter of President Trump.

The underlying notion is that in a city where Democrats outnumber Republicans six to one, the only way to defeat Mr. Mamdani is for his challengers — the three independents and Curtis Sliwa, the Republican candidate — to consolidate their support behind just one of them, and avoid splitting the vote in a five-way race.

In some ways, the calls for unity among the independent candidates echo the push that left-leaning groups made during the primary, when they urged supporters to lock arms in an effort to defeat Mr. Cuomo.

But while the leading Democratic candidates had mostly agreed to work together, there were early signs that Mr. Adams, Mr. Cuomo and Mr. Sliwa agreed only in theory — as long as it was the others who dropped out.

Mr. Adams, describing what he called Mr. Cuomo’s “arrogance,” said the former governor had asked him to bow out.

“I’m the sitting mayor of the City of New York,” Mr. Adams said in an interview on CNBC. “And you expect me to step aside when you just lost to Zohran by 12 points?”

When asked whether Mr. Cuomo should drop out, the mayor replied, “He should, he should."

Rich Azzopardi, a spokesman for Mr. Cuomo, said the campaign would not respond to Mr. Adams’s characterization to avoid discussing a private conversation. But in a statement, he argued that if all the candidates stayed in the race, it would split the vote and “all but ensures a socialist” would win the election.

“While this is unorthodox, these are unusual times,” Mr. Azzopardi said. “We are at a dangerous moment for our city.”

He added: “Mayor Adams did not run in the Democratic primary because he knew he was anathema to Democrats and unelectable. Nothing has changed. We do not see any path to victory for Mayor Adams.”

Mr. Paterson did not say whom he preferred as mayor, but he was clear that it was not Mr. Mamdani, even if he seemed to generate newfound enthusiasm among Democrats.

“If he’s the cure to what ails the party,” Mr. Paterson said, “then cyanide is the cure for a headache.” Mr. Paterson, a moderate, endorsed Mr. Cuomo in the Democratic primary but sharply criticized the candidate and his campaign after his defeat.

Mr. Sliwa said he had no plans to leave the race, suggesting that Mr. Cuomo’s loss in the primary and Mr. Adams’s widespread unpopularity made their candidacies untenable. “If the independents want to play musical chairs, be my guest,” Mr. Sliwa said in an interview. “Me, I’m focused on the campaign.”

Mr. Mamdani’s victory has been met with opposition from those on the far right, Republicans and some in the business community.

Mr. Mamdani’s campaign said the resistance was to be expected, given the right’s discomfort with his campaign promises of freezing the rent for some apartment dwellers, providing universal child care and making city buses free.

“More than 545,000 New Yorkers voted for Zohran Mamdani, the most votes any Democratic primary candidate has received in 36 years,” said Lekha Sunder, a spokeswoman for the Mamdani campaign. “In the coming months, Zohran looks forward to growing this coalition and reaching new voters with his vision for an affordable New York City.”

On Monday night, Democratic district leaders in Manhattan met with Mr. Mamdani and then endorsed him for mayor, saying in a post on X, “Democrats supporting Democrats. Groundbreaking.” In an accompanying statement, they said that they supported his vision for a more affordable city.

Next week, Mr. Mamdani has meetings scheduled with a group of chief executives from some of the city’s largest companies and other tech industry leaders, according to Kathryn S. Wylde, the head of the Partnership for New York City, a business group.

Keith L.T. Wright, the Manhattan Democratic chairman, backed Mr. Cuomo in the primary but said in an interview Monday that the former governor’s chance had passed.

“He had a good run, and the electorate spoke loudly and they spoke clearly,” Mr. Wright said. “Sometimes you’ve got to know when to show ’em and when to fold ’em.”

Rodneyse Bichotte Hermelyn, a state assemblywoman who leads the Brooklyn Democratic Party, backed Mr. Cuomo in the primary but now supports Mr. Mamdani after his victory. She said the effort against Mr. Mamdani would only serve to make his “base stronger and bigger.”

But other Democrats who supported Mr. Cuomo in the primary and remain opposed to Mr. Mamdani said in interviews that it was untenable for both the mayor and former governor to keep running, though they declined to say what they thought should happen instead.

“When he makes his decision, then I’ll make my decision,” H. Carl McCall said of Mr. Cuomo, his former rival turned ally.

Mr. Cuomo’s remaining allies argue that he has the better shot of defeating Mr. Mamdani. But his campaign would face real practical limitations. In the primary, for example, he relied extensively on large labor unions, like the ones representing hotel workers and doormen, to run his get-out-the-vote operation.

Several unions that had supported former Gov. Andrew M. Cuomo in the primary have now switched their support to Mr. Mamdani.Credit...Hiroko Masuike/The New York Times

Those unions, and others, have switched their loyalty to Mr. Mamdani and are prepared to spend generously on his behalf. Rich Maroko, the president of the Hotel and Gaming Trades Council, said in an interview that Democrats should unite behind their nominee, Mr. Mamdani.

“New Yorkers want to see him take a shot at the job, and they want to see him in the job,” he said. “I think he’s going to be successful no matter what.”

Mr. Adams and Mr. Cuomo are also pursuing many of the same deep-pocketed donors. Both men spent the weekend in the Hamptons, the summer enclave of the city’s wealthy where Mr. Adams was raising money.

“I want the person that drives the limousine to love the city and the person in the back seat of the limousine to enjoy the city,” Mr. Adams said at one event.

Some Cuomo supporters were moving in his direction. Jeffrey Gural, a real estate investor who donated $25,000 to a super PAC supporting Mr. Cuomo’s candidacy, said he would now be backing Mr. Adams.

Mr. Walden took somewhat of a victory lap after his idea was well received by some of his opponents, even as he acknowledged that he might not benefit from it.

“If I’m one of the losers in that poll,” Mr. Walden said, “I will stick to my word and step out.”

Jeffery C. Mays is a Times reporter covering politics with a focus on New York City Hall.

Nicholas Fandos is a Times reporter covering New York politics and government.