The Obama administration hopes a new rule governing overtime pay will give assistant managers at stores and restaurants a middle-class salary and better working conditions, the nation’s top wage enforcer said Monday.

“It used to be an entry-level management position was a middle-class kind of job,” David Weil, administrator of the U.S. Department of Labor’s Wage and Hour Division, said in an interview in Westbury. But, he added, “we found lots and lots of cases where that wasn’t the case — it was barely a minimum-wage job” with people earning $30,000 a year and working 60 hours a week.

The new rule — set to go into effect Dec. 1 — requires that managers or other salaried workers earning $47,475 or less per year be paid overtime. The cutoff has been $23,660 since 2004; it will now be updated every three years.

Weil said some managers would see fatter paychecks — either by earning overtime pay or getting raises to boost their salaries above the new threshold — while others would work fewer hours and have more time with family and friends.

“If you are a manager and work more than 40 hours, you need to be compensated for overtime,” he said.

Weil was on Long Island to outline the new rule to a private meeting of company executives, union leaders, advocates for workers’ rights and representatives of business groups.

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He acknowledged that the change, unveiled in May, has drawn criticism from some groups, including the National Retail Federation and American Council on Education, which represents college presidents. They have predicted it will increase consumer prices and lead to job cuts.

Weil said the Labor Department had consulted with businesses to ensure the rule wouldn’t be burdensome, including agreeing not to change the job duties test used to determine overtime eligibility, which was set in 2004.

“I think it’s productive for the employers because a workforce that is being compensated accordingly . . . in the long run becomes more productive — they turn over less,” he said.

Weil and Irv Miljoner, the wage division’s Long Island district director, estimated more than 4 million workers nationwide will be eligible for overtime under the change. A further 9 million will receive clarity on whether their jobs qualify for overtime.

The local office has become well-known for its crackdown on area restaurants that fail to pay the minimum wage.

“The violations are rampant and they are severe,” Miljoner said. “We will continue this ongoing effort because it’s important work.”

Correction: An earlier version of this article incorrectly reported the threshold for overtime eligibility as of Dec. 1 and the year that threshold was last raised.