They voted 280 to 292 to oppose the proposal that confirmative public vote will be conducted on Brexit.
North Norfolk Liberal Democrat MP Norman Lamb had voted for a common market, and a customs union.
To be granted a further postponement the Government will have to set out what goal it would achieve and it will nearly certainly involve taking part in the European elections.
He warned that otherwise "the default legal position is the United Kingdom will leave the European Union in just 11 days time" without a deal - an option that experts have warned could cause huge economic disruption on both sides of the Channel.
As it stands, without a solution, a no-deal Brexit will set in on 12 April, less than two weeks from now.
"There is a growing expectation that a (House of) Common's majority could coalesce around a softer Brexit that includes a custom's union but she is facing more threats from cabinet members to resign if she decides to pursue a softer Brexit", MUFG analysts said. It won 273 votes but there were 276 votes against, raising hopes among its supporters that the idea could be revived.
MPs have control of proceedings in the Commons on Wednesday, but Speaker John Bercow said it was not yet clear what debates and votes will be staged.
Ian Blackford, the SNP's Westminster leader, said it would be an "outrage" if MPs were asked to vote on Mrs May's deal again, while Green Party MP Caroline Lucas said it was "dead".
Britain's exit from the European Union remains deadlocked after the House of Commons failed to agree on any alternative to Prime Minister Theresa May's divorce deal, rejecting all indicative vote options.
Responding to the result, Brexit Secretary Stephen Barclay said Parliament would now have to back May's deal.
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"I have failed chiefly because my party refuses to compromise".
Sterling rose 0.8 percent to as high as $1.3135, also finding support from better-than-expected manufacturing survey data and media reports that the opposition Labour party would support closer ties with the European Union in Monday's series of votes on parliament's favoured Brexit option.
But having promised not to lead the Tories into the scheduled 2022 election and then said she would quit before the next phase of the Brexit process, would her MPs allow her to fight another contest as leader?
Labor leader Jeremy Corbyn said it was "disappointing" that none of the proposals secured a majority, BBC News reports.
May's government is considering bringing May's deal back for a fourth vote this week.
"I think "no deal" is now highly likely".
"I regret, therefore, to announce that I can no longer sit for this party".
British cabinet ministers were once again reportedly instructed to boycott the votes as MPs make a second attempt to coalesce around an alternative deal.
However, bringing back the vote for the fourth time could prove hard, given that the House of Commons speaker has suggested he would block any move for the deal to be voted on again.
None of the Monday votes on the proposals are legally binding, meaning it will be up to the British government if they act on the results.