“This City Hall is going to be on the side of working families all over this city,” the mayor said.

Liberal groups, led by the Working Families Party, had fought for years to enact sick-leave legislation in New York City, only to be stymied by Mr. de Blasio’s predecessor, Mayor Michael R. Bloomberg, and the previous Council speaker, Christine C. Quinn, who said businesses were too overburdened to withstand the added requirements.

Mr. de Blasio has long supported sick-leave laws, but he became more outspoken as the issue came to the forefront in the mayoral race, when he started hammering Ms. Quinn, a chief rival for the Democratic nomination, over her refusal to allow a vote on the measure. Under pressure, she eventually allowed a compromise bill to pass the Council. At the time, the city’s leading business groups, who had a sympathetic ear with Mr. Bloomberg, virulently protested the passage of the bill.

Signaling New York’s political turn, those same groups on Friday issued only tepid statements, saying they hoped to work with legislators in shaping the final form of the measure.

In interviews, small-business owners offered mixed reviews when told of Mr. de Blasio’s plans.

Sunny Singh, the manager of Market Deli in Midtown Manhattan, said he employed six workers and was fearful that the requirements would be financially harmful.

“Small businesses, they cannot afford it,” said Mr. Singh, who was overseeing a busy lunch hour, adding that he did not have enough money to pay employees who were unable to come to work. “When they are sick, they don’t get paid. It’s usually like this.”

At a Manhattan branch of the nutrition retailer GNC, Sandra Cesar, the manager, said she believed her six employees deserved the benefits included in the measure. “Everybody is entitled to get sick and get paid for it,” she said.

But Ms. Cesar said she also worried that workers eager to avoid shifts could exploit the measure. “They might take advantage of it,” she said.