The Taoiseach Enda Kenny and the British Prime Minister Theresa May have held discussions on the crisis in Northern Ireland.
Mr Kenny and Mrs May spoke by phone following the resignation of Martin McGuinness, which will spark imminent elections.
Both leaders reaffirmed their commitment to the institutions and the Good Friday Agreement of which they are co-guarantors of.
Earlier, Sinn Féin has rejected an offer by the DUP leader Arlene Foster for new talks to save the Stormont Assembly.
The outgoing first minister had offered to hold talks on the format of an inquiry into the 'cash for ash' scandal.
But Sinn Féin has insisted the time for talking has passed - and it is now on an election footing.
Deputy party leader Mary Lou McDonald says there can be no deal without Mrs Foster standing aside during the inquiry.
“The fact remains that Arlene Foster has to stand aside – that has been said repeatedly, publicly.
“Currently as we speak Arlene Foster and the DUP seem to me to be living in a state of denial.
“I think they need to get over that, they need to understand that the game is up, that we are facing into elections”.
"We will take our case to the electorate"
In a statement Tuesday, Mrs Foster said: “I am no longer the First Minister so therefore there is no reason, under Sinn reins reasoning, why an investigation cannot now be established.
"I want to see an investigation commenced quickly so that it will be independently demonstrated that I did nothing wrong and that my integrity is vindicated.
“This is vitally important from a political perspective but also fundamental for me on a personal basis. I have been quite disgracefully maligned in the most viscous manner and therefore it is of the utmost importance that the truth comes out.
“If necessary we will take our case to the electorate and use it as a platform for further discussions.”
The issue resolves around a controversial Renewable Heating Incentive (RHI) scheme.
It was designed to encourage businesses to replace older heating sources with more eco-friendly alternatives.
But a lack of cost controls meant businesses were receiving more in subsidies than they were paying for renewable fuel, and the scheme was drastically oversubscribed.
It came to a head Monday, when the Deputy First Minister Martin McGuinness announced his resignation.
Northern Ireland Secretary of State, James Brokenshire, has said that unless Sinn Féin nominates a replacement in the next seven days, he would have to call an assembly election.
