DUP Leader Arlene Foster arrives at DUP head quarters in East Belfast on Tuesday , The day after Martin McGuinness resigned as Northern Ireland's deputy first minister in protest against the handling of a botched energy scheme that could cost taxpayers £490m. Photo Colm Lenaghan/Pacemaker Press

DUP leader Arlene Foster arrives at DUP headquarters on Belmont Avenue in east Belfast. The RHI Scandal continues at Stormont with Martin McGuinness standing down as Deputy First Minister yesterday meaning the Assembly might have to face another election. Picture by Jonathan Porter/Press Eye

DUP leader Arlene Foster arrives at DUP headquarters on Belmont Avenue in east Belfast. The RHI Scandal continues at Stormont with Martin McGuinness standing down as Deputy First Minister yesterday meaning the Assembly might have to face another election. Picture by Jonathan Porter/Press Eye

DUP leader Arlene Foster arrives at DUP headquarters on Belmont Avenue in east Belfast. The RHI Scandal continues at Stormont with Martin McGuinness standing down as Deputy First Minister yesterday meaning the Assembly might have to face another election. Picture by Jonathan Porter/Press Eye

DUP Leader Arlene Foster arrives at DUP head quarters in East Belfast on Tuesday , The day after Martin McGuinness resigned as Northern Ireland's deputy first minister in protest against the handling of a botched energy scheme that could cost taxpayers £490m. Photo Colm Lenaghan/Pacemaker Press

DUP leader Arlene Foster, along with her party colleagues, holds a press conference at DUP headquarters. Picture by Jonathan Porter/Press Eye

Press Eye Belfast - Northern Ireland 10th January 2017 DUP leader Arlene Foster, along with her party colleagues, holds a press conference at DUP headquarters on Belmont Avenue in east Belfast. The RHI Scandal continues at Stormont with Martin McGuinness standing down as Deputy First Minister yesterday meaning the Assembly might have to face another election. Picture by Jonathan Porter/Press Eye

DUP leader Arlene Foster, along with her party colleagues, holds a press conference at DUP headquarters on Belmont Avenue in east Belfast. The RHI Scandal continues at Stormont with Martin McGuinness standing down as Deputy First Minister yesterday meaning the Assembly might have to face another election. Picture by Jonathan Porter/Press Eye

DUP leader Arlene Foster, along with her party colleagues, holds a press conference at DUP headquarters in east Belfast. Picture by Jonathan Porter/Press Eye

Northern Ireland's outgoing First Minister Arlene Foster has said she is open for discussions with Sinn Fein as she called for a public inquiry into the failed Renewable Heating Incentive (RHI) scheme.

Martin McGuinness resigned as deputy First Minister of Northern Ireland on Monday over Mrs Foster's refusal to stand aside during an investigation into the green energy scheme.

The move by Mr McGuinness under the structure of Stormont's Executive Office also forces Mrs Foster from office.

Speaking at a press conference on Tuesday the DUP leader called for an investigation into the RHI to be set up under the 2005 Inquiries Act. That would mean a public inquiry which would compel witnesses to attend and documents to be produced.

She said that it was important that the "truth" came out.

The DUP leader has said she hopes the process of getting the inquiry under way can start by the end of the week.

She said: "I am no longer the First Minister so therefore there is no reason, under Sinn Fein's reasoning, why an investigation cannot now be established.

"If, however, Sinn Fein are still unwilling to allow an investigation to be established I intend to ask for an investigation, on the basis of the terms of reference discussed as part of our discussions with Sinn Fein, to be set up under the Inquiries Act 2005.

"I am determined that the public will get the facts in an independent and impartial way free from party political demands and bias.

"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."

Mrs Foster said that Economy Minister Simon Hamilton would be speaking later this week on cost controls over the failed scheme.

"Detailed work on cost controls is ongoing and material will be sent to the Department of Finance.

"We want any draft legislation to bring spending into line and the Minister for the Economy will consult with other parties on this. Simon will, later this week, have more to say on both transparency and cost controls."

Mrs Foster said that she remained opened to further discussions with Sinn Fein and the other political parties.

She said: "If necessary we will take our case to the electorate and use it as a platform for further discussions. I have never taken the verdict of the electorate of Northern Ireland for granted and while an election is not of our making we trust the judgement of the people."

Reacting, Sinn Fein MLA Michelle O’Neill said the crisis of confidence in the institutions "has gone way beyond the RHI scandal".

“This is an act of desperation by the DUP," she said.

“If the DUP were serious about addressing the political crisis then Arlene Foster would have stepped aside a month ago as Martin McGuinness suggested privately to her. They refused to do so and arrogantly attempted to brazen out the public anger.

“Arlene Foster did not remove herself from office, Martin McGuinness removed her to allow the people to have their say."

She said Mr McGuinness made it clear that "the status quo is not an option".

“We will not be re-nominating a Deputy First Minister before the election,” she added.

Earlier Northern Ireland Secretary of State James Brokenshire told the House of Commons that the current situation in Northern Ireland is grave and that the clock was ticking on an election.

As he urged the political parties to find a way around the current impasse, he said it was "entirely premature and unhelpful" to talk about the suspension of the devolved institutions.

The state-funded RHI was supposed to offer a proportion of the cost businesses had to pay to run eco-friendly boilers, but the subsidy tariffs were set too high and, without a cap, it ended up paying out significantly more than the price of fuel.

This enabled applicants to "burn to earn" - getting free heat and making a profit as they did it.

Belfast Telegraph