It had barely been two months since Adrienne Adams became the last Democrat to join the New York City mayoral primary race when she got a call from a number she did not recognize.

It was Zohran Mamdani, the 33-year-old state assemblyman who had stormed to second place in the polls. He broached the idea of the two cross-endorsing each other.

Ms. Adams, 64, the first Black person to lead the City Council, needed the help. She was working furiously to raise enough money to meet the threshold for public matching funds. She, in turn, had something Mr. Mamdani needed: support from the city’s critical older Black electorate.

It may have seemed like a perfect fit, but Ms. Adams did not see it that way.

She and her advisers felt that Mr. Mamdani — a democratic socialist who has made campaign vows to make buses free, open city-owned grocery stores and freeze the rent for some apartment dwellers — was too far to the left and would alienate her base of moderate Democratic voters in southeast Queens.

As the Democratic primary for mayor enters its final days, a familiar dispute is playing out between the left and the city’s crucial Black electorate. Despite being pressured to cross-endorse Mr. Mamdani, Ms. Adams seems set on doing the opposite, criticizing him during the candidates’ second debate.