Mr Trimble sought to resolve the impasse over IRA arms decommissioning by arguing for Sinn Fein to contest seats in a new Northern Ireland Assembly.
The Government has insisted that no all-party talks with Sinn Fein can begin until the IRA has at least begun decommissioning.
At a party reception in Belfast on Friday night, Mr Trimble said that, by taking part in elections to the assembly, Sinn Fein could show it is committed to the democratic process. He said he could foresee the prospect of discussions between the Unionists and Sinn Fein in the assembly.
John Major, in an interview on BBC Radio 4's Today programme, said: "I very much welcome the fact that Mr Trimble and the Ulster Unionists are making practical proposals about how we can move forward. We will want to examine what Mr Trimble has said. It will certainly bear careful examination. We will certainly look at it."
John Bruton, the Irish premier, said the plan should be "carefully studied". In a statement issued at the European Union summit in Majorca, he said: "I look forward with interest to examining the full text of Mr Trimble's proposals - and to discussing it with him. As has long been acknowledged by almost all participants, a three-stranded approach is needed if we are to find a viable settlement to the problems of Northern Ireland."
Mr Bruton and Mr Trimble are expected to meet in Dublin within the next two weeks.
Talks between Mr Major and Mr Bruton aimed at re-starting the peace process ended in deadlock yesterday, but Mr Major said it was "nonsense" to say the process was doomed.
On Thursday, Gerry Adams, the Sinn Fein president, warned that the process was "doomed to collapse" if Britain continued to insist on arms decommissioning before the Republicans could join all-party talks.
Speaking at the Majorca summit where he met Mr Bruton, Mr Major challenged Mr Adams to declare whether the refusal to lay down arms, thereby allowing the process to re-start, meant he was going to return to violence. "Are you going to return to violence? Are the IRA going to return to violence? That is the question," he said.Reuse content