Rees-Mogg's powerful cabal the European Research Group (ERG) confirmed he has submitted a letter of no confidence to the Tory party's ruling 1922 Committee.
Mrs May is set to meet Graham Brady, chairman of the committee, later this afternoon as Downing Street said she would fight any leadership challenge.
The MP for North East Somerset held a crunch meeting of the ERG as the PM defended her Brext deal in the Commons.
It is understood long-standing May critic Boris Johnson attended the meeting as the two Brexiteers wings of the party attempted to unite against the PM.
Cabinet met for five hours last night in bid to agree Mrs May's exit agreement – and this morning four ministers have resigned in protest over the plan.
Brexit-backing Tories in the ERG have gathered for a meeting in Parliament – with loud banging of tables being heard from outside as the meeting of the group.
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Mr Rees-Mogg's full letter reads: "A few weeks ago, in a conversation with the Chief Whip I expressed my concern that the Prime Minister, Mrs Theresa May, was losing the confidence of Conservative Members of Parliament and that it would be in the interest of the Party and the country if she were to stand aside.
"I have wanted to avoid the disagreeable nature of a formal Vote of No Confidence with all the ill will that this risks engendering.
"Regrettably, the draft Withdrawal Agreement presented to Parliament today has turned out to be worse than anticipated and fails to meet the promises given to the nation by the Prime Minister, either on her own account or on behalf of us all in the Conservative Party Manifesto.
"That the Conservative and Unionist Party is proposing a Protocol which would create a different regulatory environment for an integral part of our country stands in contradistinction to our long-held principles.
"It is in opposition to the Prime Minister's clear statements that this was something that no Prime Minister would ever do and raises questions in relation to Scotland that are open to exploitation by the Scottish National Party."
COUP: Jacob Rees-Mogg has launched a bid to overthrow the Prime Minister (Pic: GETTY)
Prominent Eurosceptic Tory MP Andrea Jenkyns, who previously threatened to trigger a leadership contest over the Prime Minister's Brexit plans, tweeted:
"From what MPs are telling me, more letters have gone in. I have even had current ministers tell me that in a vote of no confidence they would vote Theresa May out.
"She can fight it. But I am confident she will not win it. Time to save Brexit and our party with a new leader."
Alistair Burt, the pro-European Foreign Office minister, expressed fury at the scenes inside the ERG as the group moves to oust Mrs May.
He said: We are working our socks off and they are doing everything they can to detonate it."
And an unammed former minister said: "If this coup detat succeeds, what happens then?
"The best way to defeat this deal is to defeat it in parliament, in my view."
Mr Johnson reportedly said nothing at the meeting – and declined to comment as whether he would file a letter of no-confidence.
ON THE BRINK: Can Theresa May survive this latest rebellion over Brexit? (Pic: DS)
The Prime Minister issued a rallying cry to MPs to get behind her Brexit deal “in the national interest” in a defiant speech as she clings to power.
She conceded that negotiating Brexit has been a “frustrating process” but hailed her withdrawal agreement as a “decisive breakthrough” after two years of fraught talks.
While taking questions from furious MPs, arch Brexiteer Rees-Mogg issued an audacious veiled threat to support a vote of no confidence in her leadership.
Referring to chairman of the 1922 Committee Graham Brady, he asked her: “As what my right honourable friend says, and what my right honourable friend does, no longer match, should I not write to my right honourable friend, the member of Altrincham and Sale West?”
At least 48 Tory MPs are required to send letters of no confidence to Brady in order to trigger a vote – a threshold that is rumoured to have been reached.
Mrs May announced the draft withdrawal agreement last night on the steps of Downing Street after she secured backing in a tumultuous five-hour cabinet meeting.
THREAT: Jacob Rees-Mogg outright told Theresa May in the Commons he will be take her on (Pic: SKY NEWS)
But this morning her government is falling apart after a spate of resignations, including cabinet ministers Brexit secretary Dominic Raab and work and pensions secretary Esther McVey.
Juniors ministers, among them Shailesh Vara, Suella Braverman and Anne-Marie Trevelyan, have also quit and more are expected in a day of high drama in Westminster.
Knives have been drawn by MPs across the spectrum, with Raab saying the deal amounted to “blackmail” and Labour leader Jeremy Corbyn describing it as a “botched deal”.
Yet, the PM appeared to be holding her nerve in parliament, telling MPs the British people “want us to get this done”.
“Once a final deal is agreed, I will bring it to parliament,” she told parliament amid jeers and shouts of derision from MPs.
“And I will ask MPs to consider the national interest and give it their backing.
“Voting against a deal would take us back to square one.”
BACK ME: Theresa May has called on MPs to back her Brexit in the Commons (Pic: PA)
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BETRAYAL: McVey said the deal does not respect the result of the referendum (Pic: GETTY)
Responding to her comments, Labour leader launched a savage attack on Mrs May and her drat deal, which he described as a “huge and damaging failure”.
He said: "The Government is in chaos. Their deal risks leaving the country in an indefinite halfway house without a real say.
"When even the last Brexit Secretary, who theoretically at least negotiated the deal, says 'I cannot support the proposed deal', what faith does that give anyone else in this place or in this country?
"The Government simply cannot put to Parliament this half-baked deal that both the Brexit Secretary and his predecessor have rejected.
"No deal is not a real option and the Government has not seriously prepared for it."
LEADERSHIP: Jacob Rees-Mogg has declined to run in a contest for new PM (Pic: GETTY)
Raab, who was appointed secretary of state for leaving the EU in July, said he could not “in good conscience” continue to support the draft withdrawal agreement proposed by the PM.
In his bombshell resignation letter, he said he decided to quit because Mrs Mays Brexit deal poses a “very real threat to the integrity of the UK” and he opposed an “indefinite backstop arrangement”.
In a stinging assessment, he said the draft deal, which could keep the UK tied to EU rules for the next three years and could treat Northern Ireland differently, amounted to “blackmail”.
Raab wrote in his letter to the PM: "It has been an honour to serve in your government as justice minister, housing minister and Brexit secretary.
"I regret to say that, following the cabinet meeting yesterday on the Brexit deal.
"I must resign. I understand why you have chosen to pursue the deal with the EU on the terms proposed, and I respect the different views held in good faith by all of our colleagues."
RESIGNED: Dominic Raab's exit as Brexit secretary opened the floodgates (Pic: GETTY)
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RESIGNED: Esther McVey also quit the Cabinet over Brexit (Pic: GETTY)
“Voting against a deal would take us back to square one”
Theresa May
He is the second Brexit secretary to stand down from the role in just six months after David Davis resigned from the post over Mrs Mays so-called Chequers plan.
Remain-backing Tory MP Anna Soubry tweeted: "Raab's resignation marks the end of PMs Withdrawal Agreement.
"This is very serious. The PM will clearly be considering her position.
"My own view is that we need a Govt of National Unity and we need it now."
Former Ukip leader Nigel Farage, who yesterday said Mrs May's deal was the worst "in history", said: "Well done Dominic Raab, a few more and we will be rid of this duplicitous Prime Minister."
PROTESTS: Demonstrators have flooded Parliament amid the chaos (Pic: GETTY)
Meanwhile, the EU council president Donald Tusk this morning announced that an extraordinary summit in Brussels on November 25 will take place to finalise the UKs withdrawal agreement.
Following the release of the 585-page agreement document, Jacob Rees-Mogg – the leader of the pro-Brexit European Research Group – wrote to all Tory MPs urging them to vote against it.
Rees-Mogg said that he was not among those MPs who had written to Brady, but suggested he could be "very close" to doing so.
"Certainly this has dented my confidence," he told ITV's Peston programme. "Politics depends on trust and this document is shattering to trust."
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