The Prime Minister has urged Northern Ireland's politicians to "go the extra mile" to save Stormont's crisis-hit powersharing government.
David Cameron said the Government stood ready to do what it could to resolve the political meltdown sparked by a murder linked to the IRA.
First Minister Peter Robinson and three of his four Democratic Unionist ministerial colleagues walked out of the coalition Executive in Belfast yesterday, leaving a husk of an administration limping on.
Intensive political talks involving the Northern Ireland parties and the British and Irish governments are due to start on Monday in a bid to rescue powersharing.
Mr Cameron described the crisis as an "extremely worrying situation".
Speaking in Leeds, the Prime Minister said: "We stand ready to help, including standing ready to help with getting rid of the paramilitary organisations and properly examining how they still exist, what they consist of and putting them out of commission in our country.
"I would appeal to the politicians to go the extra mile, the extra ten miles if they have to, to make these institutions work for people in Northern Ireland."
Sinn Fein Deputy First Minister Martin McGuinness today said politicians had "six weeks" to save the Executive.
DUP Finance Minister Arlene Foster has been left in the Executive to act as what her party is describing as a "gatekeeper" to prevent controversial government decisions by the remaining nationalist and republican ministers.
As well as her current portfolio, she has assumed the post of acting First Minister.
The unionist walkout from the mandatory coalition came after the DUP failed to get the Assembly adjourned for a period to allow crisis talks to address the implications of the murder of Kevin McGuigan.
The political furore over the killing intensified on Wednesday when three senior republicans were arrested in connection with the murder. The trio and a woman have been released unconditionally, police said.
As he announced the resignations, Mr Robinson repeated a demand for the Government to suspend the institutions outright to enable space for the talks to happen. Northern Ireland Secretary Theresa Villiers last night rejected the call.
Mr Cameron today insisted it would not be right to suspend the institutions.
"It is unacceptable in any part of our country to have active paramilitary groups," he said.
"They have to be disbanded, and disbanded on all sides, and it is absolutely vital and I can completely understand about the concerns that have been expressed because of what has happened in recent weeks in terms of these appalling murders.
"I want these devolved institutions to succeed, everyone wants them to succeed, so I don't think it is right for the British government, the UK Government, to step in and suspend the institutions.
"I want to see the politicians of Northern Ireland coming together, talking together, working out how to make these institutions work."
The fallout from the murder of Mr McGuigan has already seen the Ulster Unionists resign their one ministerial post.
The exit of Mr Robinson along with three of the DUP's four other ministers, and its one junior minister, has left the 13-minister administration in freefall.
The departments of health and social care; social development; enterprise, trade and investment; and regional development are now effectively rudderless.