Video report by ITV News Political Correspondent Libby Wiener
Martin McGuinness has resigned as Deputy First Minister of the Northern Ireland Executive.
It is believed he will stand down in protest at the Democratic Unionist Party's handling of a botched renewable energy scheme.
Sinn Féin believes the scheme could have cost taxpayers hundreds of millions of pounds.
Mr McGuinness announced his decision after his partner in government, DUP First Minister Arlene Foster, repeatedly refused to step down to facilitate a probe into the ill-fated Renewable Heat Incentive (RHI) - a scheme that has left Stormont facing a £490 million overspend.
Ms Foster presided over the ill-fated RHI while economy minister, although she did eventually suspend it.
The 46-year-old has refused to accede to Sinn Féin's demand for her to step aside to enable an inquiry into her actions.
ITV News Correspondent Marc Mallett reports from Belfast
Mr McGuinness has said Sinn Féin will not replace him in the role, meaning an election is inevitable.
The structure of Stormont's Executive Office means a First Minister cannot hold the position without a co-equal Deputy First Minister, effectively forcing Ms Foster from office.
The government, formed in 2007 under terms of Northern Ireland's peace accord, requires support from Sinn Féin and the DUP to survive.
Meanwhile Ms Foster branded Mr McGuinness' decision to resign and pull down the power-sharing administration as "not principled" and "purely political".
She continued that Sinn Féin's actions were motivated by politics rather than principle.
"I am disappointed that Martin McGuinness has chosen to take the position he has today.
"His actions have meant that, at precisely the time we need our government to be active, we will have no government and no way to resolve the RHI problems.
"Let me make it clear the DUP will always defend unionism and stand up for what is best for Northern Ireland and it appears from the Deputy First Minister's resignation letter that is what annoys Sinn Fein the most."
In a video posted on her Facebook page, Ms Foster said she was "disappointed that Martin McGuinness has chosen to take the position he has.
"His actions have meant that at precisely the time when we need our government to be active we will have no obvious way to resolve the RHI problems."
Sinn Féin had been due to formally call for Ms Foster to step down in an Assembly debate next week, although there had been debate the party would pull the plug earlier.
In his resignation letter Mr McGuinness wrote: "It is my firm view that the DUP's handling of this issue has been completely out of step with a public mood which is rightly outraged at the squandering of public money and the allegations of misconduct and corruption.
"The public are demanding robust action and accountability but the DUP, in particular its leader Arlene Foster, have refused to accept this."
Mr McGuinness also wrote he was resigning with "deep regret and reluctance".
The letter said: "The First Minister has refused to stand aside, without prejudice, pending a preliminary report from an investigation.
"That position is not credible or tenable...
"We now need an election to allow the people to make their own judgment on these issues democratically, at the ballot box."
Mr McGuinness' resignation comes just hours after Ms Foster accused Sinn Féin of playing a political game of chicken and warned she would not blink first.
"If he is playing a game of chicken, if Sinn Fein are playing a game of chicken, and they think we are going to blink in relation to me stepping aside they are wrong - I won't be stepping aside," she said.
"And if there is an election, there is an election."
Speaking about the reasons behind his resignation, Mr McGuinness said: "We in Sinn Féin will not tolerate the arrogance of Arlene Foster and the DUP.
"I believe today is the right time to call a halt to the DUP's arrogance."
Mr McGuinness also said his health played no part in his decision to stand down, and added that the the DUP were living in a "Fool's Paradise" if they thought they would be able to return to government with Sinn Féin after an election if the RHI issue was not resolved.
Northern Ireland Secretary of State James Brokenshire said he will work with political parties to find a way forward following Martin McGuinness’ resignation as Deputy First Minister.
“The UK Government has a primary role in providing political stability in Northern Ireland and we will do all that we can to help the parties find a resolution in the coming days.
“There is a clear process set out regarding what happens next.
"Unless Sinn Féin nominates a replacement to the position of deputy First Minister within the next seven days, it is incumbent upon me to call an Assembly election within a reasonable period.
“I would urge Northern Ireland’s political leaders to take the necessary steps to work together to find a way forward and I will work with all parties and the Irish government to this end.”
What is the Renewable Heating Incentive?
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 so.
Claims of widespread abuse include a farmer allegedly set to pocket around £1 million in the next two decades for heating an empty shed.