The Justice Secretary Liz Truss and Prime Minister Theresa May are under pressure to condemn "chilling" attacks on judges from within their own party following the High Court's ruling on Brexit earlier this week.
It comes after the High Court ruled Mrs May does not have the power to start the Brexit process by triggering Article 50 without a vote in Parliament.
She also stressed that the Government would be appealing the High Court's decision on Article 50.
A number of senior Conservative MPs had urged Mrs May to take action over a "chilling" backlash against the legal profession, warning some of the reaction had bordered on "fascist".
The judges behind the ruling have faced furious criticism after declaring Theresa May does not have the power to trigger Article 50 - the official start of the Brexit process - alone, meaning it must go to a vote in Parliament.
Bob Neill, the Conservative chairman of the justice select committee, said the backlash threatened the "independence of our judiciary" and had "no place in a civilised land".
Speaking to The Times, he said:
Some of the things which have been said about the court's judgment by politicians have been utterly disgraceful.
Former attorney general Dominic Grieve called the attacks "chilling and outrageous", and "smacking of the fascist state".
Anna Soubrey, former minister and Remain campaigner, said some media reports were "inciting hatred".
She told the Guardian: "I think we have to call this out and say 'not in my name'.
"It needs somebody like Boris Johnson to step up and speak out. He's our Foreign Secretary and he knows what the reaction of the rest of the world is as they look at our great country and are horrified.
"What message are we sending out to the rest of the world? Probably that this nation is in grave danger of losing the plot - and I think we might have done".
It comes after the shock resignation of pro-Brexit Conservative MP Stephen Phillips over "irreconcilable policy differences".
The MP said he was quitting over the government's failure to appreciate the need to consult parliament over Brexit.
He also accused the government of "shirking" responsibility for unaccompanied child refugees and the way international aid was spent.
His resignation fuelled speculation that Mrs May would call an early general election, but a Number 10 source insisted that she stood by her earlier statement that she would not call an election before 2020.