In his most sweeping bid yet to apply a focus on income inequality across the municipal spectrum, Mayor Bill de Blasio of New York on Wednesday will introduce a reimagined take on the city’s ambitious environmental program, PlaNYC.

The city is pledging to lift 800,000 residents out of poverty or near-poverty in the next decade — the largest urban poverty reduction effort ever in the country, officials said — and significantly reduce the “racial/ethnic disparities” in premature mortality. The administration will move to create some 500,000 housing units by 2040, according to the plan, and help the average New Yorker reach hundreds of thousands of jobs by transit within 45 minutes.

And with the series of lofty goals comes a new name: OneNYC, rebranding what perhaps had been the defining document of Michael R. Bloomberg’s last half-dozen years as mayor — a “sustainability and resiliency blueprint” that informed long-term policies such as carbon reduction goals and coastal protections against extreme weather.

While Mr. de Blasio has praised his predecessor’s legacy on environmental issues, some advocates have quietly complained that the emphasis on equity could dilute the program’s founding purpose in other areas.