The Rev Martin Smyth has said the onus to unify the Ulster Unionist Party was now on Mr Trimble.
Speaking after the leadership ballot on Saturday, he said he would respect the council's verdict provided Mr Trimble would adhere to party policy.
"I have stood because I believed that, in the light of his remarks in Washington, David Trimble had actually buried the UUP's policy on decommissioning. I did it, therefore, to test the mood of the party.
"The party has spoken. David is the leader. It will be his responsibility now to unify us on the policies that the party has been prepared to go forward with.
"I would certainly be loyal . . . if Mr Trimble is prepared to tell us how he is going to unify not only the council but the party in the country and beyond. Unionist voters have actually been deserting this party in droves," Mr Smyth said.
The South Belfast MP said he would watch to see what the "workable sequencing", proposed by Mr Trimble to re-establish the power-sharing executive, constituted. "If it is a departure from the concept of `no guns, no government', then I cannot support it."
Asked if Mr Trimble should contemplate resignation, Mr Smyth refused to be drawn. However, the UUP leader would no doubt be "assessing" his position in the coming days.
"He may have to make his decision very shortly on what he is going to do based on whether he feels he can carry people with him . . . I would say his political judgment has been questioned today. There are those who fear he might not even get reselected, never mind elected, in his Upper Bann constituency next time. Anything is feasible in Ulster politics."
He denied that the UUP's difficulties had done irreparable damage to the Belfast Agreement.
"I think the people who are killing the Belfast Agreement are those who have turned away from the basic commitment. Even Bertie Ahern and others have categorically said you cannot be in an executive government in a democracy having your own private army. They are the people who would destroy this agreement and I would like to think that, if they continue to do so, the governments who signed it will actually deal with them," Mr Smyth added.
The former Orange Order grand master rejected what he described as a "Trimble supporters' spin" that most of his votes had come from the Orange Order and older party members. "People talk about the old men of the party, but I want to attribute the result to the young folk, who did a lot of the footwork and the legwork."