ATLANTA — More than two dozen states challenging the health care overhaul urged a U.S. appeals court on Wednesday to strike down the Obama administration’s landmark law, arguing it far exceeds the federal government’s powers.

The motion, filed on behalf of 26 states, urges the 11th Circuit Court of Appeals in Atlanta to uphold a Florida federal judge’s ruling that the overhaul’s core requirement is unconstitutional. The judge, U.S. District Judge Roger Vinson, said Congress cannot require nearly all Americans to carry health insurance.

Allowing the law to go forward, the states argued in the 69-page filing, would set a troubling precedent that “would imperil individual liberty, render Congress’s other enumerated powers superfluous, and allow Congress to usurp the general police power reserved to the states.”

So far, three federal judges, have upheld the law. Vinson and the Virginia judge, both Republicans appointees, ruled against it. It seems certain that the broad health care challenge will be resolved only by the nation’s top court, and Vinson suggested in a March ruling that the “Supreme Court may eventually be split on this issue as well.”

The filing comes about a month after the Justice Department formally appealed Vinson’s ruling, arguing that Congress had the power to require most people to buy health insurance or face tax penalties because Congress has the authority to regulate interstate business.

The legal wrangling started when the states filed a lawsuit last year. Vinson agreed in a Jan. 31 ruling that said the entire health care overhaul passed by the then-Democratic-controlled Congress and signed by President Barack Obama is unconstitutional. It is considered the most sweeping ruling against the health care law.

His ruling followed the same reasoning as one last year from a federal judge in Virginia who struck down the insurance requirement. But the Florida judge’s ruling also invalidated provisions ranging from Medicare discounts for seniors with high prescription drug costs to a change that allows adult children up to age 26 to remain on their parents’ coverage.

At the center of Vinson’s ruling and the subsequent legal filings is the legality of the requirement that Americans carry health insurance except in cases of financial hardship. Those who cannot show they are covered by an employer, government program or their own policy would face fines from the Internal Revenue Service when the program takes effect in 2014.

The federal government argued that the requirement is a “quintessential exercise” of the legislative branch’s powers, but the states that oppose it countered Wednesday that the mandate is an “indefensible” and unprecedented move by Congress.