In a rare statement on Tuesday, Roberts wrote: "For more than two centuries, it has been established that impeachment is not an appropriate response to disagreement concerning a judicial decision."
He wrote the correct response was to file an appeal.
Roberts' statement followed Trump's call in a social media post on Tuesday for the impeachment of a federal judge.
Washington-based US District Judge James Boasberg ordered the administration on Saturday to halt the removal of alleged Venezuelan gang members, which Trump has argued is authorised by an 18th-century law historically used only in wartime.
Tensions have been rising in the eight weeks since Trump returned to the White House with the president and his allies publicly criticising courts for blocking aspects of Trump's agenda.
The combative atmosphere has raised concerns among some legal experts that the administration might openly defy a court order, possibly sparking a constitutional crisis.
At a hearing, Judge Boasberg had ordered a halt to all deportations carried out under the Alien Enemies Act, including turning around any planes already in transit.
Two planes carrying hundreds of the alleged gang members were already in the air and were not returned, prompting accusations that Trump's administration had defied the court order.
The Trump administration wrote that two flights had departed before the judge's written order was issued and that spoken orders the judge had issued in court before the written notice hit the docket were not enforceable.
"I'm just doing what the VOTERS wanted me to do. This judge, like many of the Crooked Judges' I am forced to appear before, should be IMPEACHED!!!" Trump wrote on Tuesday.
US Marshals have warned judges of heightened threats in recent weeks as administration allies have ramped up efforts to discredit judges who stand in the way of White House actions.
On social media, billionaire Elon Musk, a close Trump ally, and Republican lawmakers have described judges as threats to democracy.
Eight judges have been impeached, convicted and removed in US history, the last in 2010.
Trump's post marked the first time during his second term as president that he has called for a judge's impeachment, a move that garnered support from his Republican allies in Congress.
Just hours after Trump's post, Republican lawmaker Brandon Gill said on X that he had introduced articles of impeachment against Judge Boasberg in the House of Representatives.
Republicans control both houses of Congress but do not have the two-thirds majority needed in the Senate to convict the judge.
The statement by Roberts, a conservative who was appointed by Republican president George W Bush, echoes one from 2018, when Roberts defended the judiciary's independence after persistent attacks by Trump during his first term in office.
"We do not have Obama judges or Trump judges, Bush judges or Clinton judges," Roberts said in a statement at the time, praising "an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them".
Trump, who has appointed three of the justices to the nine-member court himself, had called a judge who ruled against his policy barring asylum for certain immigrants an "Obama judge".
The Supreme Court is weighing Trump's March 13 request asking it to intervene in his bid to curb automatic US birthright citizenship.
