The parents who sued the city over its school cell phone ban said yesterday they would appeal a judge’s decision last month to uphold it, vowing to take their case all the way to the Supreme Court if necessary.

“We will not rest until the cell phone ban is lifted,” a lawyer representing eight parents and a parents’ group, the Chancellor’s Parent Advisory Committee, Norman Siegel, said.

Schools Chancellor Joel Klein defended the ban at a City Council hearing earlier this week. “There’s no question, throughout public schools in America today … they’re using them to cheat on tests, they’re using them to dial up the Internet,” he said. He also touted a compromise plan, which would let students bring cell phones to school, but store them in outside lockers to avoid any distraction.

A department of education spokeswoman said about five schools in each borough will have such lockers next September.