Northern Ireland Secretary of State Theresa Villiers has said there is an urgent need to find a way forward so that talks can take place that will lead to the full implementation of the Stormont House Agreement.

Speaking after meeting all the parties individually today, she said there was general agreement that if the devolved institutions are to function effectively, issues arising out of continued activity by paramilitary organisations must also be addressed.

She said she will update the House of Commons tomorrow and plans to resume talks on Wednesday.

Earlier, Sinn Féin's Martin McGuinness warned that the talks cannot have preconditions attached.

Amid uncertainty over whether one-to-one meetings in Belfast involving the Executive parties and the British and Irish governments will progress to round-table negotiations, the Deputy First Minister said if full-scale talks fail, or do not proceed, then the next logical step is a snap election.

The Executive is close to collapse as a result of a crisis sparked by a murder linked to the IRA.

The Ulster Unionists have quit the Assembly and the Democratic Unionists have pulled four of their five ministers out of the administration.

UUP leader Mike Nesbitt has insisted negotiations can only proceed if Sinn Féin stops denying the IRA exists.

Mr McGuinness said: "I do think that as we enter into these discussions that it is very, very important that we do so on the basis of no preconditions.

"And I want to see, and am working for, talks to take place with a view to a successful outcome.

"But if talks are not going to take place and if talks do take place and there is no successful outcome then, in my view, the next logical step is to an election, and that is my very firm and strong view.

"Our party has no fear whatsoever of an election."

Earlier, Mr Nesbitt said Sinn Féin's attitude to whether the IRA is still in business would "kill or cure" powersharing in Northern Ireland.

Speaking after his party’s bilateral meeting with Ms Villiers at Stormont House, he urged against round-table talks until Sinn Féin's stance had been established.

"We have cautioned against holding a round-table discussion at this time until the Secretary of State gets a feel of where others, particularly Sinn Fein, are with regard to the way forward," he said.

The crisis was sparked by the murder of Kevin McGuigan last month.

Police have said current members of the IRA may have been involved in last month's shooting of Mr McGuigan in a suspected revenge attack for the murder of former IRA commander Gerard "Jock" Davison in Belfast three months earlier.

The disclosures about the IRA have heaped pressure on Sinn Féin to explain why the police assess that the supposedly defunct paramilitary organisation is still in existence.

Sinn Féin insists the IRA has gone away and has accused the two unionist parties of contriving a crisis for electoral gain.

The controversy escalated last week when three senior republicans, including Sinn Féin's northern chairman Bobby Storey, were arrested by detectives investigating the murder. All three were later released without charge.

But during the period they were being questioned, Mr Robinson stepped down and three of his DUP ministers quit the executive.

Commenting publicly on his arrest for the first time yesterday, Mr Storey accused unionists of trying to cynically exploit his "wrongful detention" to bring down powersharing.

He repeatedly insisted the IRA was no more.

PSNI Chief Constable George Hamilton has said there is no evidence IRA leadership sanctioned the McGuigan murder.

However, he said structures of the organisation still exist, albeit for political, not terror, purposes.

Mr Storey said he agreed with the assessment there was no IRA military footing, but he added: "Where I differ from the chief constable, is there is no role for the IRA, the IRA has finished, the IRA has gone.

"I think the chief constable and other perspectives out there see this in terms of the IRA being the caterpillar that's still there, where I think it's moved on, it's become a butterfly, it's flew away, it's gone, it's disappeared and they need to evolve to that as well."