Mr Trimble released the text of a letter to the Irish Foreign Minister, Dick Spring, suggesting a meeting on the same day as the next Anglo-Irish summit.
The moves coincided with a formal admission by the IRA that it planted the holdall bomb in London's West End which was defused last Thursday.
The Unionists see their initiative as a concession to Dublin which will help it to accept the idea of elections in the province as a way to all- party talks.
However, Mr Trimble did add conditions, insisting that the proposed Peace Convention in Northern Ireland - the body which would be created by elections - could not be on the agenda, since it would not "be appropriate for the Irish government to be involved in discussions relating to the creation or operation of that body".
There would have to be serious talks on substantive issues such as the normalisation of relations between the Republic and the UK in general and Northern Ireland in particular, and there would need to be a Dublin input. Mr Trimble added: "It is also desirable to discuss the consequences of the resumption of violence by Sinn Fein/IRA."
Mr Spring has twice written to Mr Trimble suggesting talks, and his first letter was rejected by the Unionist leader.
Yesterday's initiative came as a response to a second letter from the Irish Foreign Minister. Dublin has not yet responded but is likely to concur with Mr Trimble's terms.
Mr Trimble, speaking earlier on BBC Radio Ulster's Inside Politics, said that for Sinn Fein to now become involved in the talks process there would have to be a new cease-fire.
"They don't get a passport into full negotiations without a cease-fire and without an acceptance and an application and an honouring of the Mitchell Report."
He said he hoped there would be a new cease-fire but said that at the moment there was "not much ground for hope" that there would be one soon.
Loyalist paramilitary groups were mentally preparing themselves for a return to violence, David Ervine, leader of the fringe Progressive Unionist Party predicted.
"I don't think they are preparing for war, but they are getting themselves gathered, mentally, for the possibility of it," he said.Reuse content