The British government has welcomed suggestions that the UDA is considering a political future.
Northern secretary Peter Hain was responding to a Remembrance Day statement by Tommy Kirkham of the UDA-linked Ulster Political Research Group which said a two-month consultation of the membership had concluded and that contact with the government was now needed.
Mr Hain, standing alongside Minister for Foreign Affairs Dermot Ahern before party talks at Hillsborough yesterday, said Mr Kirkham's statement was "very important".
"I hope that it will be followed up by concrete action and David Hanson, my deputy minister, is going to be in touch with the UPRG to see where that leads.
"If this is a genuine political breakthrough and if the UDA is really saying they are turning their backs on violence and murder and gangsterism and go down the political road, then we are happy to take them with us." But he warned: "We need to be clear that is a statement on behalf of the whole UDA."
The two ministers were hosting talks with party delegations in advance of a fresh push for progress towards devolution expected in January.
Both Mr Ahern and Mr Hain played down a refusal by the DUP to attend. Dr Paisley's party had claimed the meetings were "for the optics" and that the real business was conducted in Downing Street and Dublin.
A party delegation is due in Dublin on Friday for talks with the Taoiseach.
Mr Ahern said: "We're fairly relaxed about who turns up today or next week.
"The fact is that there is ongoing contact with parties like the DUP."
Mr Hain explained that yesterday's meetings were "exploratory talks with the parties" and were "stock-taking, ground-clearing discussions".
Sinn Féin's chief negotiator Martin McGuinness said after his meeting with the two ministers that he was disappointed the DUP had not turned up.
He accused them of intransigence.
"It's a hardball exercise, that's all it is.
Mr Hain and Mr Ahern will hold talks with the SDLP, Ulster Unionists and Alliance parties on November 24th.