Daniel Kawczynski said the Government needed to get Theresa May's Withdrawal Agreement - which a number of ERG members continue to oppose - through Parliament if they were to ensure Britain finally leaves.
Have decided to resign from ERG. Despite excellent Chairmanship by @Jacob_Rees_Mogg who has accommodated all views I can no longer be a member of caucas which is preventing WA4 from passing. Hardcore element of ‘Unicorn’ dreamers now actually endangering #Brexit— Daniel Kawczynski (@DKShrewsbury) April 8, 2019
"I don't wish to be affiliated to a caucus ... which I now perceive to be part of the problem in actually getting the Withdrawal Agreement across the finishing line," he told the BBC Radio 4 Today programme.
"From a practical perspective there are elements now within that caucus that are preventing this Withdrawal Agreement going through and therefore inevitably that will lead to possibly no Brexit at all, and that is not something I wish to contemplate. I think we should protect Brexit."
Mr Kawczynski said he opposed a call from ERG deputy chairman Mark Francois for Tory MPs to have a vote to show they had lost faith in Mrs May, even though party rules prevent another formal leadership challenge until December.
"I do disagree with Mark Francois on that. I don't think the time has come for another leadership contest. I think we have to abide by the rules our party has set," he said.
A Government aide has said he is ready to defy the whips by addressing a People's Vote campaign rally.
Huw Merriman said it was "likely" his appearance at the event in London on Tuesday would cost him his job as an unpaid parliamentary private secretary to Chancellor Philip Hammond.
The MP for Bexhill and Battle - who backs Theresa May's Brexit deal - said he wanted to use the event to explain why he supported a confirmatory referendum on the agreement in last week's "indicative" votes in the Commons.
"It has been made clear to me that is not Government policy. My issue with that is that a week ago we were given free votes and I was allowed to vote for this concept of putting the Prime Minister's deal back to the people to get it through," he told the BBC Radio 4 Today programme.
"If I then get sacked for actually explaining the way I voted in a free vote, that to me would be a new low in democracy.
"It would be nonsensical for me to be given a free vote, to be allowed to vote the way I wish to vote, but then to explain it I would lose my position. That's politics of the madhouse and I am just not willing to go along with that."