NEW YORK — New York state will gradually raise the minimum wage for fast-food workers to $15 an hour – the first time any state has set the minimum that high.

Gov. Andrew Cuomo’s administration formally approved the increase Thursday, a move the Democratic governor announced at a labor rally with Vice President Joe Biden. Cuomo said he would work to pass legislation setting a $15 minimum for all industries, a promise that comes as more and more cities around the country move toward a $15 minimum wage.

“Every working man and woman in the state of New York deserves $15 an hour,” the governor told the enthusiastic crowd of union members. “We’re not going to stop until we get it done.”

Biden predicted the $15 wage for fast-food workers would galvanize efforts nationwide.

“You’re going to make every single governor in every single state in America look at themselves,” he said at the rally in New York City. “It’s going to have a profound impact.”

Biden said he and President Obama remain committed to raising the federal minimum wage to $12 an hour.

The wage increase for fast-food workers in New York will be phased in over three years in New York City and over six years elsewhere in the state. It will apply to some 200,000 employees at large chain restaurants.

So far, Los Angeles, Seattle, San Francisco and the California cities of Oakland and Berkeley have approved phased-in increases that eventually will take their minimum wages to $15 an hour, or about $31,200 a year.

New York’s increase was recommended by an unelected Wage Board created by Cuomo – a tactic that allowed the governor to circumvent the Legislature, where the Republican-led Senate has blocked big increases in recent years. The current $8.75 minimum is already due to rise to $9 at year’s end under a law passed by lawmakers in 2013.

Fast-food workers had pushed for the increase, noting their industry employs more low-wage workers than any other sector of the workforce. They say that unlike landscaping companies or child care services, the fast-food business is dominated by multinational companies with billion-dollar profits.