"We may or may not be able to get an agreement in which case we would have to leave the European Union without one, but we're not going to be bounced into having another referendum", he said.
Amid the Tory infighting, DUP leader Arlene Foster made it clear her party would vote against the PM's current proposals.
Johnson's criticism underscored the travails that May faces in getting any Brexit divorce deal, which London and Brussels say is 95 per cent done, approved by her own fractious party.
Johnson, the younger brother of Boris Johnson, stepped down as a transport minister Friday and called for a second Brexit referendum.
"It has become increasingly clear to me that the withdrawal agreement, which is being finalised. even as I write, will be a bad mistake", he wrote in a stinging resignation statement.
"Indeed, the choice being presented to the British people is no choice at all".
To give the public a choice between these two disastrous versions of Brexit would be a "failure of British statecraft on a scale unseen since the Suez crisis", he said, referencing the 1956 conflict against Egyptian President Gamal Abdel Nasser that is widely seen as marking the moment at which Britain formally lost its imperial role in the world. While Johnson's resignation is likely to spur critics in the Conservative Party, securing a second referendum would also require support from the Labour Party, which is yet to fully clarify its stance on a referendum and what that could entail in terms of the question put to the public.
"This is a con on the British people: there is no evidence that the kind of Brexit that we've failed to negotiate while we are still members can be magically agreed once the United Kingdom has lost its seat at the table".
Johnson, backed the Remain side during the referendum said it would be "a travesty" not to have a second referendum.
Asked whether other ministers should quit over the issue, Mr Johnson told BBC Radio 4's Today programme: "I think this is so important that it's up to MPs to take a stand". We will not under any circumstances have a second referendum.
"Boundless admiration as ever for my brother Jo", he said.
"Jo Johnson is right to resign over the Withdrawal agreement which does not deliver on the referendum but creates a vassal state".