Brexit campaign chief Michael Gove has backed the judges who ruled against the Government over the process for leaving the European Union.
The former justice secretary said that even if he disagreed with elements of the High Court decision, the three judges were "brilliant, thoughtful, wise and decent men".
His comments came as current Lord Chancellor and Justice Secretary Liz Truss continued to face pressure to intervene in the row caused by the High Court ruling that the Prime Minister must seek parliamentary approval before triggering Article 50, which formally starts the two-year countdown to Brexit.
Former lord chief justice Lord Judge said Ms Truss had a responsibility to defend the judiciary, but her comments had been "a little too late and not a lot".
Mr Gove posted a series of messages on Twitter defending the judges, who have come in for sustained attack from some newspapers and Brexit-backing politicians.
He said: "The first thing to note is that judicial independence is critical to the rule of law and any proper democracy.
"The high court judges who've ruled on Article 50 are brilliant, thoughtful, wise and decent men - their judgment deserves respect.
"G ood people can differ on their reasoning and conclusion - but I find much of it persuasive."
He added that " even if I didn't agree with elements of their reasoning" he would tread the judgment of the three men - including Lord Chief Justice Lord Thomas - "with respect".
But he stressed that a "raucous, vigorous, press is just as much a guarantor of freedom as our independent judiciary".
Lord Judge told BBC's Newsnight the "personal" attacks in the press on the judges "undermines public confidence in the judicial process".
He also raised concerns about a planned protest at the Supreme Court as it hears the Government's appeal against the ruling.
Ukip leader Nigel Farage is reported to be planning to lead a march of tens of thousands of people to the court, which is across Parliament Square from the Palace of Westminster.
Lord Judge said: " I don't think it makes any difference to the judicial decision but it does make a difference to public order.
"Let's say for the sake of argument the Supreme Court decides the high court was wrong, it will undoubtedly be conveyed as a victory for the demonstrators. It won't be but that's what will be conveyed. And if that is conveyed you've undermined the administration of justice."
Theresa May has insisted the Government remains on course to fire the Brexit starting gun by the end of March next year despite the legal setback.
The Prime Minister said she was confident the Government had "strong legal arguments" but urged the Supreme Court judges to spell out the details of what ministers have to do if it loses the appeal against the ruling.
If judges rule that an Act of Parliament is required, MPs and peers will have a series of opportunities to amend the legislation - potentially causing difficulties to the Government's timetable.
Speaking to the BBC in India, the Prime Minster insisted: " I'm clear that I expect to be able to trigger Article 50 by the end of March next year. That's what I've said consistently and I continue to work on that basis.
"We believe the Government has got strong legal arguments. We'll be putting those arguments to the Supreme Court and the Supreme Court will make its judgment."
Asked whether any proposals put before Parliament would be in the form of a Bill, the PM said: "Of course, if it were the case that the Supreme Court was to uphold the view of the High Court then of course the judgment would set out what the details were.
"At the moment they haven't specified, in terms of the High Court decision, and as I say we've got strong legal arguments we will be putting before the Supreme Court."
Mr Farage appeared to question the impartiality of the Supreme Court ahead of the hearing.
He told ITV's The Agenda: "Looking at the make-up of the Supreme Court and how many European integrationists are ... that's a real concern.
"Before this court ruling, everything was settling down very well. We had a significant number of those who voted Remain accepting the result and saying let's get on with it.
"I think it's a great shame that we have been plunged back into uncertainty by people who refuse to accept the democratic result."