The International Franchise Association, the industry's largest trade group, wants the Supreme Court to take up its challenge to portions of Seattle's $15 minimum wage law. Seattle's City Council in June 2014 voted to raise the minimum wage in increments, hitting $15 an hour by 2017 for businesses with at least 500 staffers. The $15 level is more than double the federal hourly minimum of $7.25.

The International Franchise Association and five Seattle franchisees quickly sued Seattle, which like New York City has moved to treat smaller franchised businesses like larger companies.

June 2014 file photo of Mayor Ed Murray signing a bill that raises Seattle's minimum wage to $15 an hour. Getty Images

They argued that the mandated $15 pay unfairly lumps franchised businesses with large employers. The association and franchisees want to be recognized as smaller businesses to get more time to raise pay incrementally to $15 by 2021.

Read MoreHow Seattle franchisees are fighting the $15 minimum wage

"Our appeal has never sought to prevent the City of Seattle's wage law from going into effect," franchise association President Robert Cresanti said in a statement this week. "Our appeal to the Supreme Court will be focused solely on the discriminatory treatment of franchisees under Seattle's wage law and the motivation to discriminate against interstate commerce." The association said a response is due from the city of Seattle within 30 days, and the Supreme Court is expected to announce this spring whether it will hear the case. In March 2015, a federal judge threw out the franchise groups' lawsuit, and the decision was upheld in September by the 9th U.S. Circuit Court of Appeals. For now, Seattle wages are tiered. The wages range from $10.50 to $13 an hour, depending on the size of the employer and whether the company pays toward medical benefits. A representative from Seattle Mayor Ed Murray's office could not be immediately reached for comment.