Chief negotiator Michel Barnier told the European Parliament on Wednesday that no 'alternative arrangements' for the backstop could be discussed until the Withdrawal Agreement had been signed in its current state.
On Tuesday, MPs voted on an amendment by Sir Graham Brady calling for a different backstop solution, and Theresa May is set to return to Brussels.
But Mr Barnier said the agreement had to be signed first before any alternatives could be put on the table.
He said: "We share the will of the UK Parliament to avoid a no deal.
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"I agree with Theresa May, voting against a no deal - as happened yesterday - does not rule out the risk of a no deal.
"For us, the Withdrawal Agreement remains the best and only means to ensure an orderly withdrawal of the UK."
He added: "The backstop is part and parcel of the Withdrawal Agreement and this agreement will not be renegotiated."
Mr Barnier said the backstop was "at the heart" of the EU's efforts to protect the single market after Brexit.
Criticism of deal 'hard to accept'
Responding to UK critics of the agreement, he said: "It is tough, I find it hard to accept this blame game they are trying to play against us."
Jacob Rees-Mogg accused the EU of attempting to "punish" the UK for leaving.
Mr Barnier said: "Right here and now, quite honestly, no-one on one side or the other can say very clearly and precisely what form these alternative arrangements will take so they can be operational and they can objectively meet the aims of the backstop.
"Calmly and clearly, I will say right here and now - with this Withdrawal Agreement proposed for ratification - we need this backstop as it is. Rejecting the backstop as it stands today boils down to rejecting the solution which has been found with the British. But the problem remains."
Mr Barnier said the EU "is ready and will continue to be ready to be more ambitious" in negotiating a future economic relationship with the UK.