The main nationalist opposition party in Northern Ireland has called for joint London and Dublin rule if attempts to establish devolution fail after elections to the Stormont assembly.

As the British prime minister, Theresa May, and Irish taoiseach, Enda Kenny, pledged on Wednesday to work together to deal with the political crisis caused by the resignation of Martin McGuinness as deputy first minister, the Social Democratic and Labour party suggested that joint authority should be imposed if an administration in Belfast could not be formed.

Colum Eastwood, the SDLP leader, said if the parties in the assembly failed to piece together a devolved administration, there could be no return to direct rule with London-based ministers in charge of the region.

The demand for joint authority will be bitterly opposed by the Democratic Unionist party and Ulster Unionist party. The UUP sits with the SDLP on the opposition benches at Stormont, and the former’s leader, Mike Nesbitt, has previously suggested that the two parties could offer an alternative government to the outgoing DUP-Sinn Féin coalition.

Eastwood said: “If post election an executive cannot be formed, the only acceptable position for the nationalist community is joint authority between the Irish and British governments. We cannot allow a DUP-run government to be solely replaced by British direct rule ministers.

“Theresa May, the British secretary of state [for Northern Ireland, James Brokenshire] and the DUP need to understand that there can be no return to what has gone before.”

He added: “Joint authority allows a balance of voices between the two traditions on this island. That balance is the basis of all our agreements and it is the accommodation we all signed up to. In the absence of a functioning assembly and executive, that balance can only be served through joint authority.

“This is particularly important in the context of Brexit.

“In the absence of an executive, British direct rule would mean we are at the mercy of a hard Brexit British government. Joint authority will mean we have a voice at the Brexit table, a voice that could stand against attempts to ignore the will of our people, a voice that could represent the interests of the entire island and represent the majority of the people in the north, who voted to remain in the European Union.”

Sinn Féin has ruled out any 11th-hour negotiations to prevent elections to the assembly, saying it was “not interested” in crisis talks suggested by the outgoing first minister and DUP leader, Arlene Foster.

Speaking after meeting Brokenshire, Sinn Féin’s Michelle O’Neill said: “What we need is fundamental change. We believe the public need to have their say.

“There’s been a disrespect to the public by the DUP over a number of weeks and months in relation to [the green energy crisis], a disrespect for the public in relation to listening to the views and the concerns out there.”

The line advocated by Sinn Féin means that on Monday next week, the assembly will likely be dissolved and elections will have to take place within eight weeks.

Given the renewed rancour between Sinn Féin and the DUP, piecing together a new coalition to run a devolved administration is likely to be challenging.

McGuinness, the former chief negotiator for Sinn Féin during the peace process that led to the Good Friday agreement in 1998, said on Monday he was leaving his post because of Foster’s refusal to stand down temporarily from her job over the renewable heat incentive (RHI).

Serious questions have been raised by opposition parties about the “cash for ash” scandal, which could cost taxpayers up to £500m.

Foster had been under pressure to stand down for the duration of a proposed independent inquiry into the RHI.

Under the scheme, large financial incentives were offered to farms, businesses and other non-domestic consumers to use biomass boilers that mostly burned wooden pellets, as well as solar thermal and heat pumps.

In February 2016, a whistleblower claimed that the scheme was being abused and one farmer had made at least £1m from renting an empty shed with one boiler.

Sinn Féin initially refused to take part in a vote of no confidence against Foster last December, tabled by opposition parties. But it came under intense pressure internally to take a stronger line against the DUP, resulting in McGuinness’s resignation.

There are doubts as to whether he will stand for re-election as deputy first minister. McGuinness appeared weak and ill during the press conference announcing his resignation, and reports in Dublin suggest he has a rare heart condition.

A spokesman for Kenny said: “The taoiseach and prime minister agreed that the situation is very serious. They agreed that the two governments would work closely over the coming period.

“The taoiseach and prime minister agreed to maintain close contact ahead of Theresa May’s planned visit to Dublin at the end of January.”

The Irish foreign affairs and trade minister, Charlie Flanagan, and Brokenshire have scheduled a series of meetings with parties in the assembly in an attempt to find a solution to the crisis.

