The UK needs to "pause and reflect" before doing something "irrevocably stupid" over Brexit, Jo Johnson said a day after quitting as a minister.
On BBC Radio 4's Today he called again for another referendum, saying what was being offered fell "spectacularly short" of what had been promised.
The ex-transport minister said it would be a "democratic travesty" to not have another vote.
He denied his actions amounted to a coup against the prime minister.
Mr Johnson, who voted to remain in the EU in the 2016 referendum, stood down as Theresa May's prospective deal with Brussels was being presented to Cabinet ministers.
Mr Johnson warned the UK faced a choice between "vassalage" under her proposals and "chaos" if it left the EU without a deal.
The MP for Orpington in Greater London said he had "happily taken the decision" to end his own ministerial career and, when asked if he thought other ministers would resign, he said if they thought it was right thing for them to take a stand then "good on them".
Cabinet ministers have been invited this week to read the UK's draft withdrawal deal with the EU. Mrs May has said the withdrawal deal is 95% done - but there is no agreement yet on how to guarantee no hard border in Northern Ireland.
Downing Street has insisted there will not be another referendum "under any circumstances".
Asked whether he agreed with Mr Johnson's call, Labour leader Jeremy Corbyn said: "Not really, no. The referendum took place. The issue now has to be how we bring people together, bring people together around the principles of our economy, our rights."
He said Labour would hold the government to account over any Brexit deal put to the Commons and could still vote against it.
'Johnson says what others mutter'
By Ben Wright, BBC political correspondent
Jo Johnson's resignation feels like a very significant moment.
Here is a former Remain-supporting Conservative minister saying what others mutter privately about Brexit.
His lacerating criticism of the government's negotiation and call for another referendum has opened another flank in the Tory party for Theresa May to worry about.
Tory whips know many (40, 50, more?) Brexiteers are threatening to vote against any deal she gets from the EU in the Commons because they think it ties the UK too closely to the EU.
But the whips must also worry about Remainer Tories determined to derail the whole thing because of the costs they fear Brexit will inflict on the country.
With no majority in the Commons, No10's task could have just got harder.
Mr Johnson's resignation also fires up those in all parties who say another referendum is now needed - a suggestion again slapped down by Downing Street.
But right now, in the middle of this remembrance weekend, Mrs May will be relieved his resignation has not prompted others to follow him out of government.
There has been no domino effect, yet.
But while Westminster waits for the PM to put her final Brexit blueprint before the Cabinet for approval, these are febrile days.
In a resignation statement on Friday, Mr Johnson, who is the brother of former foreign secretary and leading Brexiteer Boris Johnson, argued Britain was "on the brink of the greatest crisis" since World War Two, saying what was on offer wasn't "anything like what was promised".
Mr Johnson told Today: "My view is that this is so different from what was billed that it would be an absolute travesty if we do not go back to the people and ask them if they actually do want to exit the EU on this extraordinarily hopeless basis."
Asked if his brother had lied to voters during the referendum, he said: "In the campaign there were undoubtedly promises made that have shown to be undeliverable. No-one can dispute that.
"It was a false prospectus. It was a fantasy set of promises that have been shown up for what they were. We are now faced with the reality of that in the form of a deal the prime minister is about to bring back before parliament."
He added he had become "deeply concerned" about the potential impact of a no-deal outcome while a minister.
Conservative MP and leading Brexiteer, Jacob Rees-Mogg, and the former First Secretary of State Damian Green, both rejected another referendum.
Mr Green told Today it "would be divisive but it wouldn't be decisive", and all the evidence showed the country was "still, more or less, split down the middle".
Mr Rees-Mogg said Mr Johnson was "re-heating 'Project Fear' to stop us leaving".
Mr Johnson is the sixth minister in Theresa May's government to resign specifically over Brexit, following David Davis, Boris Johnson, Philip Lee, Steve Baker and Guto Bebb.