A spokesperson for European Council President Donald Tusk said the withdrawal agreement is not open for re-negotiation.
It comes after MPs in the House of Commons voted in favour of an amendment calling for the Irish Brexit backstop to be replaced with "alternative arrangements".
The so-called Brady amendment was passed by 317 votes to 301 votes.
It does not specify what the alternative arrangements should be, but adds that MPs support "leaving the European Union with a deal and would therefore support the withdrawal agreement subject to [a backstop] change".
It comes after Theresa May urged MPs to give her the "strongest possible mandate" to return to Brussels and renegotiate the Brexit withdrawal deal.
However, she must now work to convince the EU to reopen talks, as European officials - including French President Emmanuel Macron - continue to insist the previously agreed deal is not up for renegotiation.
In a statement after tonight's vote in Westminster, a spokesperson for Donald Tusk said: "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.
"If the UK's intentions for the future partnership were to evolve, the EU would be prepared to reconsider its offer and adjust the content and the level of ambition of the political declaration, whilst respecting its established principles."
Mr Tusk's comments were also echoed by the Irish Government, which swiftly insisted that the withdrawal agreement is not open for re-negotiation.
In a statement, the Government said: "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."
However, it adds: "A change in the UK red lines could lead to a change in the Political Declaration on the framework for the future relationship, and a better overall outcome."
Speaking after the vote, Theresa May said: "It is now clear there is a route that can secure a substantial and sustainable majority in this house for leaving the EU with a deal.
"We will now take this mandate forward and seek to secure legally binding changes to the withdrawal agreement that deal with concerns on the backstop while guaranteeing no return to a hard border between Northern Ireland and Ireland."
She acknowledged "limited appetite" in the EU for a change, and "negotiating it will not be easy".
Earlier, MPs rejected a call for Brexit to be postponed by six months if no deal has been reached by the end of next month.
That amendment, put forward by Labour's Yvette Cooper and others, was defeated by 321 votes to 298.
MPs did, however, back a non legally binding agreement amendment rejecting the UK leaving the EU without a withdrawal agreement.
That 'symbolic' motion was passed by 318 to 310 votes.
They were among seven amendments chosen by John Bercow for tonight's vote, which followed the rejection of the withdrawal deal in the House of Commons earlier this month.
MPs also rejected a motion by Labour leader Jeremy Corbyn, who was calling for a House of Commons vote on options to avoid a no deal Brexit.
Leave and remian flags fly alongside EU and British flags opposite the House of Parliament. Picture by Claire Doherty/SIPA USA/PA Images
Opening the debate earlier this afternoon, Mrs May said she wants to work towards a deal that she knows can pass in parliament.
She said: "That means sending the clearest possible message - not about what this House doesn't want, but what we do want."
However, any effort to renegotiate the withdrawal deal and the backstop will require the agreement of the EU - and the bloc has repeatedly shot down that prospect.
Earlier today, French President Emmanuel Macron claimed the deal is 'not renegotiable'.
The EU's deputy chief negotiator Sabine Weyand yesterday warned that the Brexit Withdrawal Agreement will not be re-negotiated.
She insisted that the agreement was “very much shaped by the UK negotiators” and said British attempts to reshape it were “a bit like snatching defeat from the jaws of victory.”
She also stated that the EU remains unanimous in its belief that any time-limit to the backstop would render it useless.