Mr. Cuomo, the former governor of New York, has vowed to run a more energetic campaign than he did in the mayoral primary, and aimed to demonstrate that on Tuesday.

In the weeks since the primary, several prominent donors who had been supportive of Cuomo pledged their support to Adams in the general election, including billionaire hedge-fund managers Dan Loeb and Bill Ackman, both of whom have become so entwined with the Adams operation that they have helped vet campaign hires.