She said they also had credibility and standing from across the community.
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Ms Villiers said the three appointees collectively had an in-depth knowledge of security issues, legal expertise, an understanding of Northern Ireland politics and political structures.
However, Democratic Unionist leader Peter Robinson, who took part in the talks less than 24 hours on from being discharged from hospital after suffering a bad reaction to heart medication, said it was vital the process examined paramilitary links with “political parties in government”.
“I will be working and continuing to work with determination with the Prime Minister, the Northern Ireland parties and colleagues in the Northern Ireland government to get a way through these crises and find a resolution to the hugely important challenges we now face”.
Lord Carlile of Berriew, a Lib Dem member of the House of Lords, will sit on the panel established as part of the Government’s response to the political crisis at Stormont sparked by a murder linked to the IRA.
The 53-year-old was shot dead in a suspected revenge attack for the murder of his one-time associate and IRA commander Gerard “Jock” Davison, 47, three months earlier.
But Sinn Fein has accused the DUP of exploiting the police investigation into McGuigan’s death, claiming it was using the issue in a struggle with the rival Ulster Unionist Party.
That assessment has shone the spotlight on Sinn Fein and exerted pressure on the republican party to explain why security chiefs assess that the supposedly defunct paramilitary organisation is still in existence.
On Friday, the Government announced an independent assessment of paramilitary criminality and pledged increased funding to tackle cross border organised crime such as fuel laundering and smuggling.
They will look at information held by the police, the National Crime Agency (NCA) and security services.
The assessment is to be published by mid-October and “will be available to inform the parties’ discussions and conclusions in the cross party talks”, Theresa Villiers said.
However, that accord is in danger of unravelling over the welfare reform issue.
“Remember – in 2007 the DUP manifesto said that “terrorist structures and weaponry must be removed before the bar to the Stormont Executive can be opened”.
At the close of the first day of talks, Ms Villiers described the exchanges as “focused and productive”.
The fallout from the shooting and the other problems besetting power-sharing – including the stalemate over welfare reform – are all on the agenda during the talks.
Numerous disputes in the Executive seemed to have been resolved last December when all the parties and the two governments signed off on a deal titled the Stormont House Agreement.
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The deadlock has resulted in a £600 million (€830 million) “black hole” in the Northern Executive’s budget which could leave Stormont financially unsustainable in the coming weeks.
