US Chief Justice John Roberts on Tuesday issued a rare public rebuke of President Donald Trump, over his call for the impeachment of a federal judge, in an extraordinary display of conflict between the executive and judiciary branches.

The rebuke from the Supreme Court's leader demonstrated how controversy over recent flights of Venezuelan immigrants has inflamed tensions over the judiciary's role, with a legal case challenging Trump's actions now threatening to spiral into a clash of constitutional powers.

"For more than two centuries, it has been established that impeachment is not an appropriate response to disagreement concerning a judicial decision," Roberts said in a brief statement. "The normal appellate review process exists for that purpose."

The rare statement came just hours after a social media post from Trump, who described US District Judge James E Boasberg as an unelected “troublemaker and agitator.”

Boasberg had issued an order blocking deportation flights that Trump was carrying out by invoking wartime authorities from an 18th century law.

"This judge, like many of the Crooked Judges' I am forced to appear before, should be IMPEACHED," Trump wrote in a Truth Social post.

The White House has been sharply critical of district courts which have blocked some of the president's executive actions but this was the first time Trump has personally called for a judge's impeachment since he took office in January.

Federal judges are nominated by the president for life and can only be removed by being impeached by the House of Representatives for "high crimes or misdemeanors" and convicted by the Senate.

Impeachment of federal judges is exceedingly rare and the last time a judge was removed by Congress was in 2010. (Agencies)