Stormont remained deadlocked on Tuesday over the introduction of Irish language legislation ahead of Monday's deadline for the nomination of the North's first and deputy first ministers.
Sinn Féin has asked the UK government to intervene to bring forward the legislation at Westminster but said it would not nominate a deputy first minister without it.
If the positions are not filled, an executive cannot be formed, collapsing the Stormont Assembly and forcing an election.
Asked by the BBC if Sinn Féin would nominate a deputy first minister without such intervention by the UK government, Sinn Féin MP Chris Hazzard replied: "No, there's simply no basis for powersharing if we don't have movement on these issues.
“Powersharing was returned on the basis that we had partnership working, and that means people need to be faithful to the agreements we made.
"We can't do politics here in the North of Ireland on bad faith and broken promises. Sin é."
The SDLP said on Tuesday it would seek to introduce language and culture laws for the North at Westminster next week if the deadlock over Irish language legislation is not resolved.
Party leader Colum Eastwood said the party's MPs would table amendments to legislation due to come before Westminster that would bring forward the language and cultural provisions agreed in the New Decade, New Approach deal in 2020.
Lewis’s intervention
In a video message shared on social media on Tuesday night, the Northern Ireland secretary Brandon Lewis said it was "vital" the culture and language provisions agreed in the deal were "provided for and implemented in full."
Mr Lewis, who held meetings with the Stormont parties on Tuesday, said he would “continue to engage closely” with them and explore “all the options available”.
He did not address the request that legislation be brought forward in Westminster, and instead reaffirmed his commitment to the Stormont institutions.
The people of Northern Ireland, he said, “deserve, and I believe, want, a stable, mature, functioning Executive.
“History has shown us that political stability can never be take for granted. We all have a responsibility to protect it ... and I’ll continue to work with the parties to deliver on that,” he said.
Responding to a tweet by the SDLP on social media, the former Northern Ireland secretary Julian Smith MP gave his backing to the proposal, saying it was "good to see every effort is being made to deliver the cultural package – any vote for the cultural package at Westminster will have my full support."
However, the DUP warned the UK government against legislating on matters that it said were Stormont’s responsibility, with the DUP peer Nigel Dodds telling the House of Lords that “for Westminster to impose its will on the Assembly on devolved matters would be totally unacceptable and would lead inevitably and inexorably to a collapse in confidence in devolved institutions”.
No time frame
The legislation at the centre of the dispute is part of a number of cultural measures agreed by the five parties in the Northern Executive and the Irish and British governments as part of the New Decade, New Approach agreement, but that have not been implemented.
The new DUP leader, Edwin Poots, has said he will implement all outstanding aspects of the deal, but has not given a time frame or committed to do so within the current Assembly mandate, the key demand from Sinn Féin.
On Tuesday the leaders of five of the Stormont parties – Alliance, the Green Party, People Before Profit, the SDLP and Sinn Féin – signed a joint letter calling on the Northern Executive and the Irish and British governments to “urgently agree and publish a timetable” to pass the legislation by the end of the mandate.
