European Council president Donald Tusk said the Withdrawal Agreement is "not open for renegotiation".
In a statement, a spokesman said: "We welcome and share the UK Parliament's ambition to avoid a no-deal scenario.
"We continue to urge the UK government to clarify its intentions with respect to its next steps as soon as possible.
READ MORE: Brexit debate: MPs vote for Withdrawal Agreement if Irish border backstop replaced
"The Withdrawal Agreement is and remains the best and only way to ensure an orderly withdrawal of the United Kingdom from the European Union.
"The backstop is part of the Withdrawal Agreement, and the Withdrawal Agreement is not open for re-negotiation."
The Irish Government said the Withdrawal Agreement is not open for re-negotiation.
In a statement issued following the outcome of tonight's Westminster votes the government said: "The EU position on the Withdrawal Agreement, including the backstop, is set out in the conclusions of the December meeting of the European Council. It has not changed."
"The Withdrawal Agreement is not open for re-negotiation."
"The agreement is a carefully negotiated compromise, which balances the UK position on customs and the single market with avoiding a hard border and protecting the integrity of the EU customs union and single market.
READ MORE: MPs back Theresa May's bid to change Brexit plan
"The best way to ensure an orderly withdrawal is to ratify this agreement."
Liberal Democrat leader Sir Vince Cable said: "The House of Commons has given contradictory instructions, both ruling out no deal and setting the Government on a collision course with the EU, ramping up the chances of no deal.
"Willing the ends but not the means for preventing no deal gets us nowhere.
"Parliament remains effectively deadlocked. The only way forward is a People's Vote, with the option to remain in the EU."
French President Emmanuel Macron also said the agreement was "not renegotiable", in comments just moments before MPs voted.
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