The “clock is ticking” on a Northern Ireland election following the resignation of Martin McGuinness, the Secretary of State has said.
The grave situation made an assembly election look “highly likely”, said James Brokenshire.
Mr McGuinness quit as deputy first minister on Monday over the handling of a botched energy scheme.
Meanwhile, Arlene Foster said she has been “disgracefully maligned in a most vicious manner” over the scheme.
Speaking at a press conference at DUP headquarters in Belfast on Tuesday, she said she believed there was still room for optimism.
An inquiry into the flawed scheme that could cost taxpayers £490m could get under way by the end of the week under the 2005 Inquiries Act, said the DUP leader..
“It is of the utmost importance that the truth comes out,” she said.
Under Northern Ireland’s power-sharing agreement, she loses her role with the departure of the deputy first minister.
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In a week’s time, the Northern Ireland Secretary will have the power to set a date for a new election.
Both the British and Irish governments have urged Sinn Féin and the DUP to enter talks to resolve the dispute, and Mrs Foster said she was open to such a discussion.
Irish Foreign Minister Charlie Flanagan has urged both sides to act responsibly to protect the institutions of the 1998 Good Friday Agreement.
Mr McGuinness said he wanted to “call a halt to the DUP’s arrogance”.
Sinn Féin have not disclosed details of his recent illness, but it has been reported by RTÉ that he has a rare heart condition.
Mr McGuinness denied that the decision had anything to do with health problems.
Speaking on RTE radio, Sinn Féin’s Gerry Adams said the question of who led the party into any election was a matter for Mr McGuinness.
Mrs Foster said she was disappointed by his resignation, which she said was “not principled”.
Mr Brokenshire told the House of Commons that both Westminster and the Irish government will “continue to provide every possible support and assistance to the executive parties”.
“We do, however, have to be realistic. The clock is ticking,” he said.
“If there is no resolution, then an election is inevitable despite the widely held view that this election may deepen divisions and threaten the continuity of the devolved institutions.”
Mr McGuinness cited the Democratic Unionist Party’s (DUP) conduct over the RHI scandal as the main reason for his resignation.
Mr Brokenshire said that the scheme was an “entirely devolved matter” for the Northern Ireland Assembly.
However, he added that it is “imperative that a comprehensive, transparent and impartial inquiry” is established “as quickly as possible”.
Earlier, DUP MP Jeffrey Donaldson said he was unsure whether power sharing could be restored in Northern Ireland, even after an election.
He told RTÉ he was “not convinced” that coalition government could happen in the next few months, adding that an election would not resolve the issues.
Sinn Féin’s Máirtín Ó Muilleoir said that power sharing could be restored if “the DUP commit to the principles of the Good Friday Agreement”.
“We will never rebuild credibility in these institutions unless we commit again to the promise, to the principles and to the parity of esteem that is at the very foundation and root of the Good Friday Agreement,” he said.
He accused the DUP of “trampling” on the agreement.
The RHI scandal has held centre stage in politics in Northern Ireland over the past month, with Mrs Foster facing repeated calls to resign – all of which she rejected.
Mrs Foster set up the Renewable Heat Incentive (RHI) scheme in 2012 when she was enterprise minister.
It was an attempt by the NI Executive to increase consumption of heat from renewable sources.
But businesses received more in subsidies than they paid for fuel, and the scheme became heavily oversubscribed.