The remarks marked the first public response by Roberts to Trump over the Republican president's frequent criticism of the federal judiciary. Opponents of Trump have called his criticism of judges an attack on the rule of law in the United States.

"We do not have Obama judges or Trump judges, Bush judges or Clinton judges," Roberts, a conservative who was appointed by Republican former president George W. Bush, said in a statement released on Wednesday by the Supreme Court in response to a news media inquiry.

"What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them. That independent judiciary is something we should all be thankful for," Roberts added.

It is unusual for a US chief justice, who presides over the nine-member US Supreme Court, to issue such a statement in response to a president. The US Constitution established the federal judiciary as a co-equal branch of government with the executive and legislative branches as part of a system of checks and balances on power.

Trump on Tuesday took aim at US District Judge Jon Tigar in San Francisco, who on Monday temporarily blocked an order by the Republican president that barred asylum for immigrants who enter the country illegally from Mexico, the latest courtroom defeat for Trump on immigration policy.

Tigar was appointed by Democratic former president Barack Obama.

Though Trump was reacting to the ruling by Tigar, he also blasted the entire San Francisco-based 9th US Circuit Court of Appeals, which hears appeals from federal courts in nine western states including California.

Trump called the 9th Circuit unfair and a "disgrace". That court has ruled against Trump's administration in several high-profile cases including his travel ban targeting people from several Muslim-majority countries and his bid to rescind a program that protects from deportation hundreds of thousands of illegal immigrants brought into the country as children.

"Everybody that wants to sue the United States, they file their case in the 9th Circuit, and it means an automatic loss no matter you do, no matter how good your case is," Trump said on Tuesday.

Judges in that region have also blocked construction of the Keystone XL pipeline project Trump has championed, and his administration's effort to restrict the military service of transgender troops.

In the asylum case, Tigar issued a temporary restraining order against the asylum rules, calling them an "extreme departure" from prior practice.

Australian Associated Press