The Unionist leader made it clear that while he would be meeting the Sinn Fein president he would not be shaking hands with him. Mr Adams described this approach as "rather negative."
The two leaders also made it plain that they remain poles apart on the ever-contentious issue of arms de-commissioning. Mr Trimble maintains that there must be de-commissioning before Sinn Fein can be allowed to sit in the new shadow executive; Mr Adams argues that the Good Friday agreement makes no such stipulation.
All of this could make for a frosty first encounter today, especially since some members of the Ulster Unionist party are opposed to any such meetings.
Today's meeting will take the form of roundtable talks, convened by Mr Trimble in his role as First Minister designate, of all Assembly party leaders. This will be followed tomorrow or Wednesday by a one-on-one meeting as part of a series of bilaterals between Mr Trimble and other parties.
With the first prisoners due to be released within days, possibly on Wednesday, it promises to be an argumentative week.
The weekend also brought reminders of the continuing violence, with the death of a 29th victim of the Omagh bombing as well as serious injuries to an RUC officer during loyalist rioting in Portadown.
The Omagh victim was Sean McGrath, a 61-year-old retired businessman who had been in a critical condition in Belfast's Royal Victoria Hospital since the explosion.
Mr McGrath, who lived a couple of miles outside the Co Tyrone town, leaves a wife and four grown-up children.
Two women remain in a critical condition, while a further 29 injured are still in hospital.
The RUC officer who was critically injured on Saturday night suffered extensive head injuries during an attack by loyalists following some hours of intermittent violence in the centre of Portadown.
A second officer was also in hospital with leg injuries after seven blast bombs were thrown at a group of police.
On Saturday, Mr Trimble briefed his party executive on his approach in meeting Mr Adams, but later four of his MPs issued a statement claiming no endorsement had been either sought or given for a bilateral meeting with Sinn Fein.
Executive member Arlene Foster said: "At the executive meeting there were various voices expressing concern about such a meeting. There are a lot of irate people; I don't want people to think I have okayed this."
The Trimble camp said no vote had been taken, but that "the sense of the meeting" was in support of the move.
Mr Trimble said the meeting was "very strong in endorsing our position with regard for the need for some de-commissioning to begin before we can see Sinn Fein included in a shadow executive."
He added that he would be telling Mr Adams he could not enter into a government with Sinn Fein unless de-commissioning had started.
Mr Adams said yesterday that de-commissioning was a problem, but added: "Problems have to be seen as matters which have to be resolved, as opposed to obstacles.
"The Good Friday agreement is very clear on the issue of de-commissioning - it is part of the overall process of conflict resolution, but it is not a pre-condition; it is not a pre-requisite.
"Nowhere in the agreement is the issue of decommission a pre-condition," said Mr Adams.Reuse content