Pro-Brexit International Trade Secretary Liam Fox warned of a "political tsunami" if the Government fails to deliver on the 2016 referendum vote.
He also accused MPs of trying to "steal" the result of the referendum from the people.
His warning comes as two groups of rebel MPs made moves to rewrite the Commons rule book in an attempt to derail Britain’s withdrawal from the EU.
Downing Street also hit out at the moves by MPs who are said to be planning to table amendments to enable backbenchers to take control of the business of the House to frustrate Theresa May’s Brexit plans.
One group led by Tory former minister Nick Boles and the senior Labour MP Yvette Cooper is attempting to block a no-deal Brexit – something Mrs May strongly opposes.
However The Sunday Times reported that a second group led by the former attorney general Dominic Grieve wants to go further and suspend the Article 50 withdrawal process.
Writing in The Sunday Telegraph, Dr Fox said: “Failure to deliver Brexit would produce a yawning gap between Parliament and the people, a schism in our political system with unknowable consequences.
“The reaction of the Question Time audience could become a political tsunami. It is time for MPs to deliver on the promises they made. It is a matter of honour and a matter of duty.”
Dr Fox also hit out at ministers calling for Mrs May to rule out a no-deal Brexit, saying the “most stupid thing possible” in a negotiation is to “give away your strongest card”.
Appearing on BBC One's The Andrew Marr Show, Dr Fox said politians were trying to "hijack" Brexit.
He told Andrew Marr: "You've got a leave population and a remain Parliament, Parliament has not got the right to hijack the Brexit process because Parliament said to the people of this country we make a contract with you, you will make the decision and we will honour it."
Downing Street described the moves by MPs as “extremely concerning” and said they underlined the need for politicians who supported Brexit to vote for it in the House.
“The British public voted to leave the European Union and it is vital that elected politicians deliver upon that verdict,” a No 10 spokeswoman said.
“Any attempt to remove the Government’s power to meet the legal conditions of an orderly exit at this moment of historic significance is extremely concerning.
“This news should serve as a reminder to those MPs who want to deliver Brexit that they need to vote for it – otherwise there is a danger that Parliament could stop Brexit.”
But Labour former minister Hilary Benn dismissed the reports and denied MPs were plotters, telling BBC One's The Andrew Marr Show that politicians were "just doing their job".
"They are trying to sort out the mess the Prime Minister has created," he added.
Mr Benn said he would be in favour of a second referendum to break the impasse in Parliament but believed MPs had "an obligation to try and honour the first".
The report comes as Mrs May prepares to brief Cabinet ministers on her talks with other party leaders and senior MPs following the crushing defeat of her Brexit deal last week in the Commons.
The Sunday Times said it had obtained leaked emails showing that Mr Grieve had been in secret communication with a Commons clerk of bills Colin Lee to discuss how it could be possible suspend Article 50.
In one email sent on Wednesday, Mr Lee was said to have made clear that the aim of the plan was to delay Brexit.
“What follows is just for you and you will understand the terms,” he said.
“We have been thinking that legislation is needed, but it occurs to me the substantive motion, say calling for Article 50 extension, could be made.”
In a statement, a House of Commons spokesman said: “It is common practice for clerks to provide advice to Members on the drafting of many items of parliamentary business, such as bills, motions and amendments.
“This advice is provided on a rigorously impartial basis. We do not comment on individual cases.”
Mrs May is due to make a statement to MPs on Monday setting out how she intends to proceed with Brexit after the tumultuous events of last week.
She will also table a “neutral” motion – which is expected to attract a flurry of amendments from MPs – which will be debated and voted on on January 29.
In a letter to the Telegraph, 50 Tory association chairmen and other senior grassroots figures said the party’s 2017 manifesto stated “no deal was better than a bad deal”, and failing to honour that pledge would be a “breach of trust with with voters and party members”.