Belfast’s political crisis will not delay the triggering of Article 50 and Britain’s exit from the European Union, Theresa May has said.

It comes after the Northern Ireland Deputy First Minister Martin McGuinness resigned on Monday, effectively ending power sharing at Stormont. The Sinn Fein politician cited concerns over the DUP’s “arrogance” in how it has handled allegations of a major financial scandal, known as the “cash for ash” affair.

Unless a replacement for Mr McGuinness is found within seven days a snap election will be triggered for the devolved Northern Ireland Assembly. The next election had been scheduled to be held in 2021.

But the SNP’s Westminster leader Angus Robertson called on the Prime Minister to postpone triggering Article 50 – the untested protocol for leaving the EU – if voters go to the polls because it would leave Northern Ireland voiceless in the Brexit process.

“In these circumstances will she postpone Article 50 or will she just plough on regardless?” he asked.

But Ms May said she wanted a swift resolution to the political crisis in Northern Ireland, adding: “It is still the case that ministers are in place and that obviously there are executives in place, that we are still able to take the views of the Northern Ireland people.”

Shortly after Prime Minister’s Questions, Ms May’s spokeswoman said she understood Stormont ministers would continue to hold their positions in a caretaker role during any election.

The spokeswoman added: “Obviously the situation is in flux and we are doing all we can to try to find a way through, including by the PM speaking to the Irish Taoiseach last night about the situation.

“There is now a window before elections could be called, and we are not going to get ahead of ourselves. We have been clear on the timetable for triggering Article 50 and we will be sticking to that.”

She added: “We are going to focus on how we can support political stability in Northern Ireland, recognising the progress that’s been made and not wanting to put that at risk and engaging with all the parties.”

A Labour spokesman said the party wanted a Commons debate on the Government’s Brexit negotiating position “as urgently as possible” and before the invocation of Article 50.

The crisis in Northern Ireland “can’t be allowed” to derail Mrs May’s plan to table Article 50 by the end of March, added the Labour source. “We are not in any way seeking any such delay... we won’t do anything to frustrate the passing of Article 50 – we’ve made that clear time and again – and we don’t want delay in it.”

During a phone call on Tuesday Ms May and the Irish Taoiseach, Edna Kenny, according to Downing Street, recognised the difficulties and seriousness of the situation.

A spokesperson added: “In addition, they spoke about how the Northern Ireland Secretary and the Irish Minister for Foreign Affairs and Trade, Charlie Flanagan, will be working very closely together over the next few days and months to support the parties of Northern Ireland in finding a resolution.

“The Prime Minister also said how important it was to make sure that Northern Ireland’s voice and interests are heard as we prepare to leave European Union and how the Northern Ireland Secretary is fully committed to making this happen.

“She added that it was still our intention to hold a Joint Ministerial Committee at the end of the month to bring the devolved nations together in getting the best deal for the whole of the United Kingdom.