THE UUP leader, Mr David Trimble, last night welcomed the response of the British Prime Minister, Mr John Major, to the Hume/Adams initiative.
"What I found helpful in his attitude was the very clear indication that a mere tactical ceasefire would not trigger off any process for Sinn Fein/IRA.
"We would have to have a genuine ceasefire, with the stated purpose of it being a permanent end to the conflict, and of course time would be needed to assess that."
The UUP leader said there would also have to be a "process" in which assurances by Sinn Fein and the IRA would have to be tested against their actions.
The leader of the Democratic Unionist Party, the Rev Ian Paisley, said: "They have moved in the direction that Mr Hume wanted them to move. Now, they haven't moved fully in that direction. Whether they will stop the pace there or not, I do not know."
The Progressive Democrat spokesman on Northern Ireland, Mr Des O'Malley, said that Mr Major's statement was "reasonable".
"The British government, in the circumstances, has gone as far as its perilous parliamentary situation allowed it to go in trying to encourage a positive response. That response should now be forthcoming by the declaration of a genuine ceasefire.
"It is abundantly clear that Sinn Fein are free to join talks in a short time if they take the obvious step. Why are they not prepared to give up violence?"