That phrase created a stirring of interest, given that progress has been in such short supply lately on the questions of IRA arms decommissioning and the formation of a new Northern Ireland executive. The fact that the two sides had agreed to meet again was also seen as important.
Mr Trimble and Mr Adams were accompanied by their deputies, John Taylor and Martin McGuinness.
Earlier yesterday Mr Adams also met Mo Mowlam, the Secretary of State for Northern Ireland. Ms Mowlam gave the parties an ultimatum to resolve the decommissioning issue by the week of Good Friday (29 March to 2 April) when she will begin the transfer of powers to the Stormont Assembly.
Emerging from the meeting, Mr Adams said it was a "mistake" for the British Government not to transfer powers to the Stormont assembly now, as earlier envisaged.
It was announced yesterday that the Northern Ireland political development minister, Paul Murphy, has invited two representatives from each party to round-table talks tomorrow on how to advance the peace process. This is seen as part of a government attempt to bring fresh momentum to the process leading to intensive negotiations in the last week of March.
Speaking after yesterday's meeting Mr Trimble described the encounter as significant, though he added that the extension of the political deadline from the original target date of 10 March had meant it was "a bit of an anti-climax". He went on: "I have, throughout this process, been confident about the underlying trend of events. I'm also confident about what will ultimately happen, namely that this process will succeed. We've made it clear throughout this that the requirement for decommissioning applies to Loyalist and republican paramilitaries."
The Unionist leader added: "Paramilitaries know in their hearts, even if they are not prepared to say so publicly, that they must decommission. It's not a question of whether, it's a question of when."
Mr Adams urged all sides to use the next few weeks to make progress. He said: "There is a huge responsibility on the British Government to implement this Agreement. There is a huge onus on the Irish government and there is also a huge onus on all the other political leaderships in this situation.
"The delay has not been helpful and unless people assert themselves to fulfil the agreement then the people who voted on this island for changes on this island are going to be the people who are sorely disappointed and the only people who will be satisfied with that are those who want the peace process to fail."
Mr Adams confirmed that he had been informed of a death threat to him in recent days and said he was taking the warning seriously. But he added that it would not deflect him, or the Sinn Fein leadership, from pursuing their current policy.Reuse content