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 has the best chance of defeating Mr. Mamdani, a candidate whose 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.