(Pablo Martinez Monsivais/AP Photo)

In a remarkable, partisan exchange in a Texas courtroom Tuesday, a federal judge demanded that the Obama administration formally explain recent statements by President Obama that some have construed as questioning the authority of courts to review, and potentially strike down, his signature health care law.

Judge Jerry Smith of the 5th Circuit U.S. Court of Appeals, a Reagan appointee, issued the order during oral arguments in a case challenging the Affordable Care Act's restrictions on physician-owned hospitals.

"I would like to have from you by noon on Thursday… a letter stating what is the position of the Attorney General in the Department of Justice in regard to the recent statements by the President - stating specifically, and in detailed reference to those statements, what the authority is in the federal courts in this regard in terms of judicial review," Smith told a government lawyer in a recording of the hearing released by the court.

"The letter needs to be at least three pages, single-spaced and it needs to be specific," he added.

Smith was responding to statements Obama made Monday at a Rose Garden press conference, when he said in response to a question that it would be "an unprecedented and extraordinary step" if the Supreme Court overturned a law that was passed by "a democratically elected Congress."

"I would 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 - and passed law," Obama said. "Well, there's a good example, and I'm pretty confident that this court will recognize that and not take that step."

Obama's argument clearly unsettled Smith, who just moments into the presentation by DOJ lawyer Dana Lydia Kaesvang interrupted to voice his displeasure.

"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?" he said.

"Yes, your honor. Of course there would need to be a severability analysis, but yes," Kaesvang replied, sounding surprised by the random question.

Smith didn't back down explaining that Obama's statements had "troubled a number of people who have read it as somehow a challenge to the federal courts or their authority or the concept of judicial review, and that's not a small matter."  He also referred to the law in question as "Obamacare," an informal reference that has been politically charged.

Kaersvang again reiterated the administration's deference to judicial review, but Smith was not satisfied, moving to demand an annotated explanation 48 hours from now.

Neither spokesmen for the White House nor Department of Justice would comment on the matter.

Speaking at an Associated Press luncheon today, Obama appeared to try and clarify his position, arguing that it's been decades since the Supreme Court struck down a law on an economic issue, such as health care.

"The point I was making is that the Supreme Court is the final say on our Constitution and our laws, and all of us have to respect it," he said, "but it's precisely because of that extraordinary power that the Court has traditionally exercised significant restraint and deference to our duly elected legislature, our Congress."

You can listen to full audio of the exchange HERE:

ABC News' Jason Ryan contributed to this report.