The EU has rebuffed Theresa May’s demand for a 12-month time limit to the Irish backstop despite weeks of talks, but has tried to persuade MPs to back the prime minister’s Brexit deal by emphasising that technology could solve the Irish border problem.

In response to May’s calls for assurances that the UK would not be trapped indefinitely in a customs union, a long-awaited letter from the EU’s most senior officials, published on Monday, reiterated a commitment to examine the solutions backed by Brexiters.

Jean-Claude Juncker, the European commission president, and Donald Tusk, president of the European council, vowed in a joint letter that “facilitative arrangements and technologies” could be considered as a viable alternative to the backstop.

They also said the bare-bones customs union in the backstop need not be the basis of a future deal, even if the UK did fall into the arrangement owing to the lack of an alternative plan.

But the letter failed to offer the prime minister anything on her central call for a 2021 deadline for ending talks on the future relationship to ensure that the backstop would not last more than 12 months, if it were ever triggered.

The outcome led the Democratic Unionist party’s Nigel Dodds to complain to May in the Commons that, despite her promises, “nothing has changed”, leaving May on a trajectory towards a heavy defeat when her deal is put to a vote on Tuesday evening.

Under the withdrawal agreement’s Irish backstop, the UK is to fall back into a customs union with the EU should there not be an alternative way to avoid a hard border on the island of Ireland by the end of the transition period, which could last between 21 months and nearly four years.

The DUP and a large cohort of Tory Brexiters remain concerned that the UK will be trapped in a permanent customs union, which would kill off hopes of Britain pursuing an independent trade policy.

Juncker and Tusk offered May a helping hand by emphasising that Brussels would regard such a customs union to be a “suboptimal” trading relationship if it is triggered. Should it come about, they pledged to have six-monthly summits to check on progress on an alternative arrangement to replace it, such as a comprehensive trade deal.

“The commission is committed to redouble its efforts and expects the same redoubled efforts from your negotiators, with the aim of concluding a subsequent agreement very rapidly,” the letter states.

The letter’s further insistence that a customs union need not be the permanent solution for avoiding a hard border will be welcomed by Downing Street.

Dominic Raab resigned as Brexit secretary in November partly over his concern that the all-UK customs union envisaged in the backstop would be the basis of the future deal, as is suggested in the text of the political declaration on the future relationship.

“The European commission also shares your intentions for the future relationship to be in place as quickly as possible,” the EU officials wrote. “Given our joint commitment to using best endeavours to conclude before the end of 2020 a subsequent agreement … the commission is determined to give priority in our work programme to the discussion of proposals that might replace the backstop with alternative arrangements. In this context, facilitative arrangements and technologies will be considered.”

The EU additionally pledged to start negotiations on a trade deal as soon as possible after the UK parliament backs it, and to bring it provisionally into force even before the parliaments of the 27 EU member states have fully ratified its terms, in order to give MPs confidence that the backstop will not need to be triggered.

But the failure to secure a legal guarantee on temporary nature of the backstop was still perceived by many in the Commons, including the DUP, to be a major failure by the prime minister, given the commitments she made on delaying the last vote and seeing off a leadership challenge.

May had suggested in a letter to the EU’s leaders that this had been her main objective. She wrote: “We have said we that we will use our best endeavours to have the future relationship in place by the end of 2020, and (separately) in the text of the [backstop] protocol we have agreed the same obligation to reach an agreement that supersedes it. I hope you agree that we should have completed this process by the end of 2021 at the latest.”

The EU leaders, in response, insisted they were “not in a position to agree to anything that changes or is inconsistent with the withdrawal agreement”, and did not provide such a deadline.

Tusk and Juncker did seek to soften the appearance of the backstop by noting that regulatory alignment between Northern Ireland and the EU would not go beyond what “is strictly necessary to avoid a hard border”.

The Northern Ireland executive, which is currently suspended, would also be able to send members to the UK delegation to the joint committee, a body to oversee the withdrawal agreement.