Conservative MPs told the backbencher to “shut up” after he issued a major threat to the Prime Minister to push ahead with Brexit.
Mr Rees-Mogg, frequently tipped as Mrs May’s successor, said that any backsliding over the issue could result in splitting the Tories.
Ahead of a crunch Cabinet meeting at Chequers on Friday, he said: “Theresa May must stand firm for what she herself has promised.”
In response a number of furious Tory MPs lashed out and urged him to support the Prime Minister or “pipe down”.
Foreign Office minister Sir Alan Duncan accused Jacob Rees-Mogg of “insolence” and said his comments risked “debasing” the Government.
Writing on Twitter, the angry Remainer added: “The Prime Minister must be given maximum latitude and backing.
“The ideological right are a minority despite their noise and should pipe down. I have total support for May and the UK.”
Business minister Richard Harrington said: “I do wish people would stop putting their own dogma above the good of the country and the party.”
Another minister, Alastair Burt, added: “Enough. Just tired of this endless threat and counter threat.
“Why don’t we want the best for the UK than for our own ideological cliques?”
North Dorset MP Simon Hoare said Mr Rees Mogg, head of the pro-Brexit European Research Group, was “simply wrong”.
He said: “The hectoring nonsense and blackmail has to stop. Tories are common sense pragmatists, not dogmatic vestal virgins.”
Veteran Tory MP Sir Nicholas Soames, the grandson of Winston Churchill, told the Brexiteer-Mogg to “shut up”.
The Mid-Sussex MP tweeted: “A message for my old friend Jacob Rees-Mogg: shut up.
“Let the PM do her job without this constant carping. Put a sock it in.”
Other Tory MPs, including Richard Benyon and Paul Masterton, also piled in as the Tory infighting continued.
Mr Rees-Mogg sparked the backlash after claiming Mrs May could collapse the Government and leave the Tories in the political wilderness.
He said: “One former Tory leader, Sir Robert Peel, decided to break his manifesto pledge and passed legislation with the majority of his party voting the other way.
“This left the Conservatives out of office for 28 years. At least he did so for a policy that works.
“At Chequers, Mrs May must stick to her righteous cause and deliver what she has said she would. She must use her undoubted grace to persevere.”
Responding to Mr Rees-Mogg’s comments, Theresa May‘s spokesman said: “Our focus is on delivering the will of the British people.
“The Prime Minister has set out what she wants to achieve – that is to leave the single market, leave the customs union, leave the jurisdiction of the ECJ and be free to sign and implement trade deals around the world.”