Mr Martin McGuinness of Sinn Féin has called on all parties to develop a "positive agenda" and said the political process is entering a critical time ahead of the Assembly elections scheduled for May. The next six to eight weeks were critically important, he said.
"Any suspension of the elections or putting off of those election would be effectively a suspension of the democratic process, and that would be very damaging indeed," the Mid Ulster MP and former education minister added.
"I think all of us at the heart of this process know the best way forward is to try and resolve our problems over the course of the coming six to eight weeks and to move forward together with a very positive agenda into those elections."
He told the BBC it was time to give leadership to the people, rather than create a political vacuum, by developing a "positive and constructive frame of mind" and added that the coming weeks were perhaps the most critical of any in the last 30 years.
The Ulster Unionist leader and former first minister, Mr David Trimble, repeated his call for the IRA to renounce violence for good.
He told the same BBC programme that Mr Gerry Adams "still hasn't got the message that they have to give up violence for good".
A ceasefire was not good enough, he warned, adding: "What has to happen is what should have happened, namely that there should be a giving up of violence, not temporarily but for good.
The Northern Secretary, Mr Paul Murphy, and the Minister for Foreign Affairs, Mr Cowen, believe round-table talks, designed to open the way for a return of devolution, can be called in about two weeks following a series of individual meetings with the parties hosted by the two governments last month.