The heated Democratic mayoral primary in New York City has been engulfed by ideological arguments over the city’s management and the leadership vacuum among national Democrats.

Similar issues are animating the party’s race for public advocate, an office that serves as a kind of municipal government watchdog.

The incumbent, Jumaane Williams, is being challenged by Jenifer Rajkumar, a state assemblywoman from Queens, and Marty Dolan, a retired insurance executive.

Mr. Williams, who is supported by leading Democratic officials and organizations, has focused much of his message on how he plans to use the office to make New York more affordable. He has also vowed to ward off the threat of President Trump’s anti-immigration policies, especially given Mayor Eric Adams’s perceived cooperation with those efforts.

An Emerson College survey last month showed Mr. Williams more than 40 points ahead of his two challengers, with roughly 15 percent of voters still undecided. As a heavy underdog, Ms. Rajkumar, his main rival, has gone into attack mode.

While she has discussed her plans for how she would use the office, she has also questioned Mr. Williams’s progressive views and whether they match the city’s current political mood.