Any attempt by Theresa May to give her MPs a veto on the controversial Brexit backstop for Northern Ireland would amount to “ripping up the withdrawal agreement”, EU officials have warned.

Brussels sources told The Independent that the move, designed to convince wavering Tory rebels to vote for the treaty next week, would start a new row with the bloc and potentially jeopardise the whole deal.

Speaking on Thursday morning, the prime minister said the backstop would not be “automatic” and she was considering giving MPs a say on whether it came in.

The pledge appears to be Ms May’s latest attempt to convince her MPs to vote for the deal at a crunch sitting of the Commons on Tuesday. A survey of parliamentary arithmetic currently shows it will be rejected by a large margin.

One Brussels official told The Independent: “We hope they’re not going to try this because it’s the same as ripping up the withdrawal agreement.”

Throughout talks the EU and Irish government insisted that any border backstop would have to be “all-weather” and could not have a time-limit or other get-out clauses. The bloc’s negotiators spent months in negotiations ruling out various mechanisms to end it early.

The purpose of the legal mechanism is to prevent a hard border between Northern Ireland and the Republic of Ireland no matter what else happens in Brexit talks.

The policy would keep the UK tied to the EU’s customs territory after it left and ramp up checks on some goods crossing the Irish sea. Both sides agree a hard border must not reappear because of the Good Friday agreement.

Unionist critics say the backstop is a breach of UK sovereignty because there would be checks between Northern Ireland and the rest of the UK, while Tory MPs fear it could be used to tie Britain indefinitely to a customs union, which they do not want.

Under the withdrawal agreement, if there is no other trade deal that would allow frictionless trade by 31 December 2020, both sides have agreed that the “backstop solution will apply until such a time as a subsequent agreement is in place”.

But to avoid the backstop, the UK can instead request an extension of the transition period – which effectively keeps the UK following all EU rules as if it was still a member, without any say on them.

This extension can only be for a maximum of two years, and would have to be agreed by a “joint committee” of the EU and UK – meaning the EU could have a veto. As such, the backstop would automatically come into force under the withdrawal agreement, unless the EU agrees to prolong the transition.

This makes Theresa May’s suggestion of a parliamentary lock on the backstop either hollow – or in violation of the withdrawal agreement.

Also speaking on Thursday, the EU’s Brexit negotiator Michel Barnier insisted the agreement was the only one on offer.

In a speech at the European Committee of the Regions, he said: “I must say once again, today, calmly and clearly: it is the only and the best possible agreement.”

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The prime minister is understood to have discussed the latest veto plans with small groups of rebels in a desperate bid to get them to change their mind ahead of the Commons showdown.

She aired the plan publicly for the first time on Thursday morning, telling BBC Radio 4’s Today programme: “The backstop is talked about as if it’s automatic. Actually it is not automatic – there is a choice.