The US attorney general, Eric Holder, has bowed to a federal judge's demand that the Obama administration formally acknowledge the right of courts to strike down unconstitutional laws following the president's admonishing of the "unelected" supreme court over as it considers his healthcare reforms.

Judge Jerry Smith, who is hearing a healthcare case at a court in Houston, demanded the justice department write "a three-page letter" affirming the supremacy of the courts in deciding the constitutionality of legislation after Barack Obama said on Monday it would be an "unprecedented, extraordinary step" for "an unelected group of people" on the supreme court to overturn the healthcare law "passed by a strong majority of a democratically elected Congress".

Holder, in a letter to Smith on Thursday that ran to two-and-a-half pages, said the administration is not challenging the authority of the courts.

"The longstanding, historical position of the United States regarding judicial review of the constitutionality of federal legislation has not changed," the letter said. "The power of the courts to review the constitutionality of legislation is beyond dispute."

But the US attorney general defended Obama's observation that the supreme court has traditionally acknowledged the import of respecting the will of the elected legislature.

"While duly recognizing the court's authority to engage in judicial review, the Executive Branch has often urged courts to respect the legislative judgement of Congress," said Holder. "The Supreme Court has often acknowledged the appropriateness of reliance on the political branch's policy choices and judgements."

Obama's comments prompted a torrent of criticism from the right.

Republican leaders accused the president of attempting to "browbeat" and "intimidate" conservative supreme court justices whose questioning of the constitutionality of a requirement for almost all Americans to have healthcare suggested they may strike down the law.

Smith told administration lawyers appearing to defend the legislation in a case separate from the supreme court challenge that he was concerned by the president's comment about "unelected judges" overturning the will 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, or to the appropriateness of the concept of judicial review. And that's not a small matter," said Smith. "So I want to be sure that you're telling us that the attorney general and the department of justice do recognise the authority of the federal courts through unelected judges to strike acts of Congress or portions thereof in appropriate cases."

Smith and two other judges sitting with him then said they wanted a response by noon on Thursday.

"The letter needs to be at least three pages, single-spaced, no less, and it needs to be specific," said Smith.

Holder responded shortly before the deadline with a letter half a page short of the judge's demand. It said that the justice department "has not in this litigation, nor in any other litigation of which I am aware, ever asked this or any other court to reconsider or limit long-established precedent concerning judicial review of the constitutionality of federal legislation."

Holder went on to address Obama's comments directly. "The President's remarks were fully consistent with the principles described herein," he said in the letter.

The Republican leader in the Senate, Mitch McConnell, earlier this week denounced the president's comments as an attempt to intimidate the supreme court.

"The president, more than anyone else, has an obligation to uphold the legitimacy of our judicial system," he said. "But his remarks on the court reflect not only an attempt to influence the outcome, but a preview of Democrat attacks to come if they don't get their way."

Obama sought to defuse the row by saying that while he respects the fact that the supreme court has the final say on the constitution and the law "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".

"The burden is on those who would overturn a law like this," the president said.

The White House maintained that the president was merely articulating a long established view of the position of the court in considering the validity of legislation passed by Congress.

The supreme court is expected to rule on the health law in June.