The Trump administration and Republicans in Congress have been waging a multifront attack on the federal judge who is deciding whether the president may use a wartime statute to deport people suspected of belonging to a Venezuelan street gang.

Lawyers for the Justice Department began the week by trying to kick the judge, James E. Boasberg, off the deportation case and then filed court papers declaring he had no authority to stop flights of immigrants from leaving the country under the law, known as the Alien Enemies Act.

On Tuesday, Representative Brandon Gill, Republican of Texas, filed articles of impeachment against the judge, accusing him of having abused his power. That same day, Mr. Trump himself endorsed the idea of impeachment, calling Judge Boasberg, a centrist Democrat who lived with Justice Brett M. Kavanaugh while they were at Yale Law School, a “Radical Left Lunatic.”

All of this — and more — prompted a rare public rebuke by Chief Justice John G. Roberts Jr. who issued a statement on Tuesday afternoon essentially telling Judge Boasberg’s critics to knock it off.

“For more than two centuries,” the chief justice said, “it has been established that impeachment is not an appropriate response to disagreement concerning a judicial decision.”

“The normal appellate review process exists for that purpose,” he added.

From the moment Judge Boasberg, 62, issued his ruling pausing Mr. Trump’s summary deportation flights on Saturday, the case has emerged as a flashpoint in a larger debate over presidential power, the use of wartime authorities to skirt normal immigration practice and the role of the courts in reviewing the actions of the executive branch.

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