The government is to publish plans later to give Stormont the power to vote against new EU rules if the border backstop comes into force after Brexit.
It comes as MPs get set to debate the withdrawal agreement ahead of a crucial vote in the House of Commons next week.
There will be five days of discussion on the terms of the UK’s withdrawal and future relations with the EU.
Cabinet Office Minister David Lidington said the plans being published were specific to NI.
Sinn Féin and the SDLP previously rejected the possibility of Stormont having a say over what kind of backstop might emerge in the event of a ‘no deal’ Brexit.
“We are publishing today a set of Northern Ireland specific proposals that make clear the continuing place of Northern Ireland within the UK internal market and which will give the Northern Ireland Assembly – as we all hope it will be reconstituted – a veto over introducing any new areas of law and policy into that backstop,” he told the BBC.
The Northern Ireland Assembly has not met for two years, but Mr Lidington said there was a real desire to restore devolution.
“Talking to MPs and leaders of all political parties at Westminster, including the Northern Ireland parties, there is a wish to get the Northern Ireland institutions back up and working again,” he said.
“When I go to Belfast or Londonderry/Derry, what I get from people in Northern Ireland and from the business community and education leaders and others, is: ‘We want our devolved institutions back again because we want a voice for Northern Ireland and we want to see both communities in Northern Ireland represented in those power-sharing institutions’.”
Both the UK and EU have agreed there cannot be a “hard border” (for example physical checks such as cameras or customs posts) between Northern Ireland and the Republic of Ireland.
This led to the inclusion of the “backstop” in the withdrawal agreement, which means a last resort plan to keep the Irish border open no matter what happens – deal or no deal.
Prime Minister Theresa May cancelled the original vote on the withdrawal agreement on 11 December.
She has since sought extra written assurances from the European leaders. The vote is scheduled to take place next Tuesday.
The Democratic Unionist Party, who Mrs May relies on for her Commons majority, has said there is “no way” that it can vote for the agreement as it currently stands.
Its 10 MPs strongly object to the backstop, a contingency plan agreed by the UK in December 2017 which the EU has said is necessary in case the two sides do not agree their future relationship or another solution by the end of 2020.
The DUP and many Tory MPs want the backstop to be removed entirely or a legal guarantee that the UK will be able to leave it unilaterally at a time of its choosing.
Without that, they say the UK faces being bound indefinitely to EU rules, curbing its freedom to strike trade deals and result in Northern Ireland being treated differently from the rest of the UK.
The Irish government has said it is willing to give further “written guarantees” to reassure MPs that the UK will not be “trapped” – although it has said the agreement cannot be changed.
Sinn Féin’s Vice-President, Michelle O’Neill, set out the party’s opposition to a possible “Stormont lock” mechanism on Brexit late on Tuesday.
She said it would be unacceptable to hand the DUP a “veto” on backstop arrangements.