The Bloomberg administration filed plans Tuesday to appeal a judge's decision to strike down a ban on the sale of large sugary drinks in New York, setting up what is likely to be a lengthy legal fight that could outlast the mayor's term in office and affect the balance of power at City Hall.

The filing came on the day the ban—the latest of Mayor Michael Bloomberg's aggressive public-health initiatives—was supposed to take effect. Instead, Mr. Bloomberg was reduced to asking restaurant owners to voluntarily comply with the...