A day after announcing a vast new inspection plan for lead in New York City public housing, Mayor Bill de Blasio on Tuesday doubled down on his administration’s commitment, vowing to “eradicate this problem once and for all.”

He said private contractors using specialized equipment would conduct inspections of every public housing apartment where lead paint might have been used — some 130,000 units — in order to create a database of those that contain lead paint and those that do not.

Maria Doulis, vice president at the nonprofit Citizens Budget Commission, said the mayor’s plan to use outside contractors for inspections was an “encouraging sign,” but added that the new spending on inspections would not address underlying management and operational issues at the sprawling Housing Authority.