The Taoiseach Leo Varadkar has said any solution to the Brexit impasse is up to Westminster.
He said he was disappointed at Tuesday night's vote in the House of Commons, which saw the withdrawal agreement be defeated by 432 votes to 202.
It was the biggest House of Commons defeat in nearly a century.
In a statement following the vote, the Irish Government said it "regrets" the outcome.
It said the result added to uncertainty and "increases the risk of a disorderly Brexit".
It has urged the UK to set out how it proposes to move forward.
"We will then consider what next steps to take in consultation with our EU partners."
The Government said it will continue to intensify preparations for a no-deal scenario.
"The Irish Government recognises, however, that a disorderly Brexit is a bad outcome for everyone, not least in Northern Ireland.
"It is not too late to avoid this outcome and we call on the UK to set out how it proposes to resolve this impasse as a matter of urgency."
As a result of the rejection, British Prime Minister Theresa May is facing a vote of "no confidence" in her government.
Leo Varadkar says he can't predict the future of Brexit. Says the ball is in Westminster's court and he doesn't believe a change of British Prime Minister would aid the process #Brexit pic.twitter.com/RKMUbVjDnT
— Sean Defoe (@SeanDefoe) January 16, 2019
"Brexit is a British policy"
But speaking on Wednesday at Government Buildings, Mr Varadkar said Brexit has to have a British solution.
"The Irish Government profoundly regrets the decision of the House of Commons to reject the withdrawal agreement between the EU and the UK, and the associated joint political declaration.
"It is not the outcome that we wanted.
"Over the coming weeks, the Government will continue to work with our European partners in a collective effort to conclude an agreement with the UK.
"The deal provides a guarantee that a hard border will be avoided, and that citizens rights and freedoms in all parts of Ireland will be protected".
He said any no-deal scenario would impact the economy - particularly farmers, fishermen and the rural economy.
He said: "A no-deal scenario would not protect the peace in Northern Ireland, so we have to work hard to avoid it.
"At the same time, our plans for a no-deal exit will continue - these are no longer contingency plans, they're being implemented by Government.
"Now businesses and other organisations, if they're not doing so, must do the same".
"We should never forget that Brexit is a British policy that originated in Westminster, after months of negotiation we found a solution - that solution has now been rejected by Westminster.
"The problem now lies there".
'Red lines'
Mr Varadkar also indicated a softening of red line issues could be mutually beneficial.
"We understand that the prime minister will now consult with other parties and other political leaders on an agreed way forward - we welcome that.
"The onus is on Westminster to come up with solutions that they can support, but they must be solutions that the European Union and Ireland can accept.
"We've always said that if the United Kingdom were to evolve from its red lines on the customs union and on the single market that the European position could evolve also."
He said that the risk of a no-deal Brexit can be avoided by an extension of the Article 50 deadline if necessary.