“New York City is the greatest city in the world, but many New Yorkers have real fears that the city they love is slipping away,” the mayor said. “From making pre-K universal to creating the safest big city in America, we have accomplished so much together, but we need to go much farther.”

The mayor pledged to legalize basement apartments to increase the city’s supply of affordable housing and to take more aggressive measures to improve street safety. He also wants to help “mom-and-pop” shops by reducing fines and approving a tax on landlords who keep storefronts vacant while waiting for high-end tenants like banks and chain pharmacies.

The speech had a format that mirrored the dozens of town halls the mayor has held while in office. Mr. de Blasio encouraged feedback from the audience, which was seated beneath a 94-foot-long blue whale at the American Museum of Natural History in Manhattan. He asked them to raise their hands if they were afraid that they would be the last generation of their family to be able to afford living in New York and if a store in their neighborhood had gone out of business. Many raised hands and nodded heads.

“This is a plan to save our city,” the mayor said as he announced new community centers and an expansion of free preschool. “And I thought long and hard about whether those words were called for, but they are.”

Still, the theme raised some questions: Save the city from whom or what exactly? (“Forces of greed,” for starters, the mayor argued.) And why didn’t Mr. de Blasio, a Democrat in his second term, start the battle earlier in his administration?