"We are called to put an end to economic and social inequalities that threaten to put an end to the city that we love," Mr de Blasio told the crowd at an inauguration hearing.
The new mayor was elected two months ago by a record margin on the promise of being a sharp break from billionaire Michael Bloomberg. Mr Bloomberg leaves office after 12 years that reshaped New York, making it one of the nation's safest and most prosperous big cities but also one that has become increasingly divided between the very rich and the working class.
Mr De Blasio, 52, called for a tax increase on the wealthy to pay for universal pre-nursery childcare. He also pledged to improve economic opportunities in minority and working-class neighbourhoods and decried alleged abuses under the police department's stop-and-frisk policy.
He and his new police commissioner Bill Bratton have pledged to moderate the use of the tactic.