If New York’s Democratic primary for mayor was to be decided by whoever had the most money and energy, Zohran Mamdani would be at a cash disadvantage but with a surplus on vigor.

He began Friday by asking the city’s Campaign Finance Board to give him a waiver to exceed the almost $8 million spending cap for the primary — hoping to come closer to leveling the huge spending advantage of his chief rival, former Gov. Andrew M. Cuomo.

Fix the City, a super PAC supporting Mr. Cuomo, has raised more than $24 million, with much of it fueling an expensive attack ad campaign against Mr. Mamdani, a Queens assemblyman and democratic socialist.

He later campaigned with Brad Lander, the city comptroller, in Prospect Park in Brooklyn, after riding there on electric Citi Bikes from Mr. Lander’s home in Park Slope. And then he ended the day with a planned seven-hour walk from the north tip of Manhattan in Inwood Hill Park to its southern tip at Battery Park, inviting his followers to join him “Forrest Gump” style.

His battle for more money, however, was destined for less traction.

The Campaign Finance Board quickly said increasing the spending cap per Mr. Mamdani’s request would be against the rules. Tim Hunter, a spokesman for the agency, said the only time the cap can be increased is when a candidate who is not participating in the matching funds program raises more money than those who are participating in the program.

That happened in the 2021 mayoral primary when Ray McGuire, one of the longest-serving Black executives on Wall Street, blew through the spending cap. It was then raised from $7.3 million to $10.3 million.