Seeking to reduce runaway obesity rates, the New York City Board of Health on Thursday approved a ban on the sale of large sodas and other sugary drinks at restaurants, street carts and movie theaters, the first restriction of its kind in the country.

The measure, championed by Mayor Michael R. Bloomberg, is certain to intensify a growing national debate about soft drinks and obesity, and it could spur other cities to follow suit, even as many New Yorkers say they remain uneasy about the plan.

“This is the single biggest step any city, I think, has ever taken to curb obesity,” Mr. Bloomberg said shortly after the vote. “It’s certainly not the last step that lots of cities are going to take, and we believe that it will help save lives.”

The measure, which bars the sale of many sweetened drinks in containers larger than 16 ounces, is to take effect on March 12, unless it is blocked by a judge. The vote by the Board of Health was the only regulatory approval needed to make the ban binding in the city, but the American soft-drink industry has campaigned strongly against the measure and vowed this week to fight it through other means, possibly in the courts.