SEATAC, Wash. — Supporters of a $15 minimum wage, approved by voters here in November but partly struck down last week by a county judge, asked the state's highest court to hear an appeal.

The SeaTac wage statute, which has been challenged repeatedly by business groups that say it will cripple businesses and lead to job cuts, takes partial effect on Wednesday, covering about 1,600 hospitality and travel workers in the city. Coverage for an additional 4,700 low-wage workers at Seattle-Tacoma International Airport, which is within city limits, was struck down on Friday by Judge Andrea Darvas of King County Superior Court, who agreed with the arguments by lawyers for the business groups — led by Alaska Airlines — that the legal reach of voters did not extend into airport property administered by the Port of Seattle.

The appeal request filed with the Washington Supreme Court hinges on that same issue, the limits of authority. Can a local government with one of the nation's busiest airports within its borders administer wage rates at airport-based companies?

"The legal question is whether the airport is a legal island," Sergio Salinas, the president of a Service Employees International Union local unit that has pushed for the SeaTac wage, said at a news conference here.

Washington already has the highest state minimum wage in the nation, at $9.32 an hour, but stands to be surpassed by California, which recently approved a $10 minimum, phased in over two years. The federal minimum is $7.25.

The SeaTac statute, which passed by 77 votes with about 6,000 cast, exempts airlines and small businesses, including restaurants with fewer than 10 employees. But Alaska Airlines, in its court arguments, has said higher costs paid by contractors would be passed along to consumers.

Tuesday's legal filing does not guarantee that the state's Supreme Court will take the case. The court may decide that a lower appeals panel should take up the matter first. But both sides have said they think the legal issues in the case will ultimately be brought to the high court.

The debate over minimum wages has recently taken on broader political dimensions, with plans by Democrats to push ballot initiatives in 2014, increasing wages — and creating opportunities to discuss economic inequality — in hotly contested congressional races. And Seattle's new mayor, Ed Murray, who pledged support during his campaign for a $15 minimum wage in Washington's largest city, last month created a committee of business and labor leaders and elected officials that will report back to him early in the year on legislative plans.