A no-deal Brexit will lead to a hard border in Ireland, the European Commission has said.
And Ireland's foreign minister Simon Coveney said Dublin would face a "very difficult job" to avoid the need for physical infrastructure on the border with Northern Ireland if Theresa May's Withdrawal Agreement failed.
The warnings came as MPs tabled amendments in Parliament to the Prime Minister's deal, the rejection of which by an overwhelming 230 votes last week has thrown into doubt proposals for a backstop to keep the Irish border open.
In a break from usual procedures, the amendments will be voted on by MPs on January 29 in another day of high Brexit drama in the Commons which could put Mrs May under intense political pressure to change course.
One plan, tabled by Tory MP Dame Caroline Spelman and Labour's Jack Dromey, would effectively rule out a no-deal Brexit.
Another, from Conservative former attorney general Dominic Grieve, would give MPs powers to take control of the parliamentary agenda on a series of days in the run-up to the official date of EU withdrawal on March 29 to pass resolutions on the way ahead.
A cross-party group of MPs, including Labour's Yvette Cooper and Tory former minister Nick Boles, is seeking to give time for a Bill to suspend the Article 50 withdrawal process if there is no new deal with Brussels by the end of February.
Labour's Hilary Benn is hoping to secure a range of indicative votes on various Brexit options.
And the chairman of the Commons Northern Ireland Committee, Conservative Andrew Murrison, put forward proposals – which he said were designed to appeal to "moderate MPs who just want Brexit sorted" – for a time limit on the backstop.
Just re-tabled my amendment to the Withdrawal Agreement. It reads; <At end add: 'but insists on an expiry date to the backstop.'>Short and sweet. Likely to appeal to moderate MPs who just want #Brexit sorted.
— andrew murrison (@AWMurrison) January 22, 2019
Labour's frontbench tabled its own amendment calling for a vote on the party's plan for a customs union with the EU and on whether to legislate for a public vote.
The move was welcomed as "a step forward" by Labour supporters of a second EU referendum including MP David Lammy, but shadow business secretary Rebecca Long Bailey insisted it did not tie the party into backing a new vote "in any way".
Speaking in Brussels, European Commission spokesman Margaritis Schinas said there was "nothing new" in Mrs May's statement to MPs on Monday, in which she promised to seek a means to keep the Irish border open in a way which can win the support of Parliament.
Asked whether the EU commitment to the peace process would last "whether or not there is a deal", Mr Schinas told reporters: "If you like to push me and speculate on what might happen in a no-deal scenario in Ireland, I think it's pretty obvious, you will have a hard border.
"Our commitment to the Good Friday Agreement and everything that we have been doing for years with our tools, instruments and programmes will have to take inevitably into account this fact.
"So, of course, we are for peace, of course we stand behind the Good Friday Agreement, but that's what a no-deal scenario would entail."
Mr Schinas said the Withdrawal Agreement sealed between the UK and EU last November was not up for negotiation, and channelled the Spice Girls as he said: "We expect the United Kingdom to tell us what they want, what they really, really want."
Mr Coveney later said: "In the absence of the backstop and a Withdrawal Agreement, we have a very difficult job to do to prevent border infrastructure, but of course that would have to be our focus."
The Prime Minister has repeatedly promised the people of Northern Ireland that the Government would do "everything in our power" to avoid a hard border after Brexit, amid fears it could undermine the peace process.
But in a TV interview earlier this month, she cautioned that this would require action to resolve issues arising from Brexit, telling the BBC's Andrew Marr: "No border doesn't happen simply because people sit around saying, 'well, we won't have a border'."
She has faced fierce opposition from Conservative Eurosceptics and the Democratic Unionist Party, who fear the backstop could trap the UK indefinitely in a customs union and force Northern Ireland to follow single market regulations.
But former cabinet minister Damian Green, a close ally of Mrs May, said he had detected signs of opinion shifting, telling BBC Radio 4's World At One: "People are now actively looking for a deal that they can support, rather than actively looking for reasons why they can't support whatever has been put forward."
Sinn Fein president Mary Lou McDonald said it was "very concerning" that Mrs May had not removed the option of a no deal from the table.
Speaking outside the Irish parliament in Dublin, she said: "As each day and as each week passes, we come perilously closer to the prospect or at least the possibility of a crash Brexit."
Green MP Caroline Lucas warned of a potential "collapse of law and order" and a threat to peace in Northern Ireland if Brexit went ahead without a deal.
Speaking at a People's Vote press conference in Westminster, Ms Lucas said: "The Government has not put 3,500 troops on stand-by to hand out plastic Union flags for everyone to wave at their no-deal Brexit street parties.
"It's put troops on stand-by to help deal with the potential collapse of law and order."
She said it was "unforgivable" for advocates of no deal to "play games with peace in Northern Ireland".