Mr Gerry Kelly, of Sinn Féin, has criticised the DUP for its refusal to accept the willingness of the IRA to tackle unionist concerns.
Mr Kelly said: "Last week the IRA set out clearly its willingness to deal with concerns within unionism, including the issues of arms and activities, in the context of a comprehensive deal."
He said the Rev Ian Paisley did not want the IRA to deal with weapons and paramilitary activity, unless it did so "exclusively on his terms and in a way which involved an unachievable process of humiliation".
He said it was bizarre that Dr Paisley was now demanding that the IRA did not deal with the issue of its weapons.
Speaking at Belfast City Hall following Wednesday's talks in Hillsborough hosted by the two governments, Mr Kelly called on Dublin and London to proceed with implementation of "the process of change".
Meanwhile, in Brussels last night, the Taoiseach and the British Prime Minister met on the margins of the EU summit to discuss the continuing impasse. A Government source said that the two had "taken stock" of the recent intensive negotiations.
Dr Mitchell Reiss, the US special envoy, continued his series of meetings yesterday. He said the progress made since the all-party talks at Leeds Castle in Kent last September was "almost unimaginable". He said the comprehensive agreement was still on the table. "I think we're all trying to figure out how we can get past the finish line here." Dr Reiss admitted there was a danger that things could "stagnate or slip backwards.
"That's why the governments are working so hard, that's why President Bush asked me to come over here this week to see if all of us - London, Dublin and Washington - along with all the political parties can try and make sure that this thing actually works."
Dr Reiss confirmed he held meetings with the Orange Order and Mrs Geraldine Finucane, widow of the murdered Belfat solicitor Pat Finucane, along with members of her family. Referring to the Orange meeting, Dr Reiss said he wanted to listen rather than talk. He confirmed Mrs Finucane had approached Dr Reiss's office in Washington earlier this year regarding a meeting and that this was his first opportunity to hear of concerns about the inquiry called by the British government into the murder.
The family have said they will no co-operate with the inquiry, elements of which are to be conducted in secret. Referring to the political situation, Dr Reiss said: "If you're not optimistic, you're in the wrong business here."
On the question of IRA decommissioning, he said: "Our position is that we're in favour of photos but against humiliation. I think that on that basis we're trying to find a way forward."