Tánaiste Simon Coveney has said that patience and calm are needed following the defeat of Theresa May's revised Withdrawl Agreement in the House of Commons tonight.
MPs rejected the British Prime Minister's Brexit deal by 391 to 242, a majority of 149.
A vote will be held tomorrow on whether they are willing for the UK to leave the EU without a deal on March 29.
If they reject no-deal, a third vote will follow – probably on Thursday – on authorising Mrs May to request an extension of the two-year Article 50 negotiation process.
It is expected that a plan for the Irish border in the event of a no-deal Brexit, as well as the no-deal tariff schedule, will be published tomorrow morning.
Reacting to tonight's vote, the Tánaiste told the BBC: “The predictions were consistent enough over the last few days that this would be a heavy defeat.
“We now need to be patient and calm to allow this process in Westminster to take its course.”
Sinn Fein President Mary Lou McDonald said the outcome of the vote shows the “absolute disregard for the people of Ireland, for our rights, our economy and the Good Friday Agreement that is at the heart of the Tory Brexit agenda”.
“The Withdrawal Agreement is imperfect but it is the only deal on offer,” she said.
“The backstop contained is a guarantee that no hard border will be imposed on this island and protects the Good Friday Agreement. We are 17 days away from Brexit and the uncertainty and confusion continues.
“A crash-out Brexit would be unthinkable for the peace process, jobs, trade and to the loss of people’s rights and quality of life, particularly in border communities.
“Despite giving assurances to Theresa May the EU has made clear that the Withdrawal Agreement is not going to be reopened for negotiation.
“There is now a need to intensify planning for a no-deal crash with an imperative to ensure no return to a hard border, protections of our agreements and safeguarding the rights of citizens," she said.
The DUP's 10 MPs voted against Mrs May's proposed Withdrawal Deal. The party's Brexit spokesman Sammy Wilson said in a tweet tonight: "Paragraph 50 has been ignored. Respect the constitutional and economic integrity of the 🇬🇧 and you will have a deal."
The defeat of Mrs May’s Brexit deal should come as no surprise, Ulster Unionist MEP Jim Nicholson said as he called for Brexit to be delayed.
“It made the division in the House of Commons a Meaningful Vote on meaningless changes," he said.
“We want a deal but we want a good deal – a deal that will not compromise the constitutional integrity of the United Kingdom.
“Calm heads are needed now and a short technical extension should be seriously considered.”
SDLP leader Colum Eastwood expressed disappointment at the vote but said Westminster will “have to accept the backstop at some point”.
Meanwhile, Alliance Party leader Naomi Long has called for a second referendum.
Business groups in Northern Ireland expressed frustration at the lack of agreement over a Brexit deal.
Aodhan Connolly, director of the Northern Ireland Retail Consortium, said: “We have no indication of customs, tariffs, documentation or checks that will be in effect on day one and we are no clearer as to the status of the border.
“There are no winners in a no-deal Brexit that systematically disintegrates the supply chains of these islands," he said.
“Politicians of all shades must put people before politics and economics before ideology to find an agreement that can pass a vote. We need a deal.”
Responding to tonight's defeat for the British PM, the EU's chief negotiator Michel Barnier said the impasse can only be solved by the UK.
In a tweet he said: "The EU has done everything it can to help get the Withdrawal Agreement over the line. The impasse can only be solved in the #UK. Our “no-deal” preparations are now more important than ever before."
The European Parliament's Brexit Coordinator Guy Verhofstadt said that instead of taking back control, the UK "spiralled out of control".
He wrote on Twitter: "Brexit was about taking back control, instead the UK spiralled out of control. Only cross-party cooperation putting Country first, can end this mess. If this happens we will fully engage. #BrexitDeal".
PA & Digital Desk
