Mr. Mamdani’s victory upended city politics and reverberated nationally. He relied on a memorable message, charisma and a strong ground game.

The president, who has a history of spewing sometimes vile insults at rivals, has in recent days escalated his attacks against the 33-year-old self-described democratic socialist. Trump has threatened to arrest Mamdani, to deport him and even to take over the country’s largest city if he wins the general election in November.