Mayor Bill de Blasio charted a robust liberal agenda for New York City on Monday, pledging to bypass Washington to address economic and social disparities by expanding benefits for illegal immigrants and pressing for a higher local minimum wage.

In his first State of the City address, Mr. de Blasio said New York would become the largest municipality to offer identification cards to residents regardless of their legal status, making it easier for undocumented immigrants to open bank accounts, lease apartments or borrow library books.

And he vowed to bring New York in line with other liberal strongholds, like San Francisco and Washington, that already set their own minimum wage, although Mr. de Blasio will need approval from legislators in Albany to enact his version.

In promising to move quickly with his plans, the mayor made clear that he had lost patience with federal lawmakers, whose efforts to enact similar policies have stagnated, and that he was undaunted by the resistance he is already encountering among officials in the State Capitol.

“We cannot wait for Washington to act,” Mr. de Blasio said. “We will not let the gridlock there — or even the limits of Albany — serve as an excuse for New York City to roll over and ignore our mission.”