Lord Chancellor Liz Truss has said it would be "dangerous" for ministers to tell the press what is acceptable to print.
Ms Truss, who is also Justice Secretary, was responding to concerns judges in the High Court case ruling on who had the final say on triggering Article 50 had suffered "abuse" at the hands of the media.
When asked about a Daily Mail headline which branded the judges involved as "enemies of the people", Ms Truss told the Lords Constitution Committee: "Where, perhaps, I might disagree, respectfully, with some who have asked me to condemn what the press are writing.
"I think it is dangerous for a Government minister to say 'this is an acceptable headline and this isn't an acceptable headline' because I am a huge believer in the independence of the judiciary, I am also a very strong believer in the free press.
"I believe, in terms of defending the judiciary, it's very important I speak out about the valuable work they do.
"But I do draw the line at saying I should be saying what is acceptable for the press to print or not. That for me goes too far.
"I will always speak out and say how important having an independent judiciary is.
"And I have also said, on the individuals involved in both cases, the High Court and the Supreme Court, that these are people of integrity, and impartiality."
The comments came after Supreme Court president Lord Neuberger complained some of the reporting of the Article 50 case risked undermining the rule of law.
Lord Neuberger also claimed politicians could have been "quicker and clearer" in defending the judiciary after the High Court ruling that Prime Minister Theresa May did not have the power to start the Brexit process without the consent of Parliament.
The Lord Chancellor told the committee it was "very serious" that only 2% of the judiciary feel valued by the Government.
"The proportion of the judiciary who feel they are valued by the Government, for example, was 2% in 2014 and it's 2% in 2016. So, that is clearly very serious.
"The percent that feel they are valued by the senior judiciary is 33% in 2014 and has gone down to 27% in 2016."
Ms Truss rejected calls for would-be Supreme Court judges to be publicly questioned before their appointment.
"I am not in favour of pre-selection hearings because what I fear they would do is lead us down a more political route."