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A federal appeals court is striking back after President Obama cautioned the Supreme Court against overturning the health care overhaul and warned that such an act would be "unprecedented."

A three-judge panel for the 5th Circuit Court of Appeals on Tuesday ordered the Justice Department to explain by Thursday whether the administration believes judges have the power to strike down a federal law.

One justice in particular chided the administration for what he said was being perceived as a "challenge" to judicial authority -- referring directly to Obama's latest comments about the Supreme Court's review of the health care case.

The testy exchange played out during a hearing over a separate ObamaCare challenge. It marked a new phase in the budding turf war between the executive and judicial branches.

"Does the Department of Justice recognize that federal courts have the authority in appropriate circumstances to strike federal statutes because of one or more constitutional infirmities?" Judge Jerry Smith asked at the hearing.

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    Justice Department attorney Dana Lydia Kaersvang answered "yes" to that question.

    A source inside the courtroom, speaking to Fox News afterward, described the questioning by Smith as pointed.

    Smith also made clear during that exchange that he was "referring to statements by the president in the past few days to the effect ... that it is somehow inappropriate for what he termed unelected judges to strike acts of Congress."

    "That has troubled a number of people who have read it as somehow a challenge to the federal courts or to their authority," Smith said. "And that's not a small matter."

    Smith ordered a response from the department within 48 hours. The related letter from the court, obtained by Fox News, instructed the Justice Department to provide an explanation of "no less than three pages, single spaced" by noon on Thursday.

    All three judges on the panel are Republican appointees.

    The Justice Department had no comment when asked about the exchange.

    White House Press Secretary Jay Carney, though, told Fox News that there's no dispute from the administration regarding the courts' authority to strike down laws.

    "Of course we believe that the Supreme Court has, and the courts have, as their duty and responsibility the ability of striking down laws as unconstitutional," Carney said Tuesday.

    However, he said the president was specifically referring to "the precedent under the Commerce Clause" regarding a legislature's ability to address "challenges to our national economy."

    The most significant Supreme Court case hinges on the question of whether the individual mandate to buy health insurance violates the Commerce Clause. The administration argues it does not.

    Though Carney said the president did not misspeak when he discussed the case on Monday, Obama was not quite so specific.

    "I'm confident that the Supreme Court will not take what would be an unprecedented, extraordinary step of overturning a law that was passed by a strong majority of a democratically elected Congress," Obama said on Monday. "And I'd just remind conservative commentators that for years what we've heard is the biggest problem on the bench was judicial activism or a lack of judicial restraint, that an unelected group of people would somehow overturn a duly constituted and passed law. Well, this is a good example. And I'm pretty confident that this court will recognize that and not take that step."

    Obama reiterated his stance on Tuesday, saying the court has traditionally shown "deference" to Congress and that "the burden is on those who would overturn a law like this."

    Carney said that Obama was expressing the point that on national economic challenges, "there should be due deference paid as a matter of precedent to our democratically elected officials."

    Click here for audio of the Appeals Court hearing on Tuesday. The exchange on the president's comments starts at roughly the 18-minute mark.

    Fox News' Shannon Bream contributed to this report.