The Ulster Unionist leader may be called before the party's ruling body to face demands for a tightening of policy on decommissioning. A decision is expected by the end of the week.
A spokesman for anti-Agreement members confirmed that the required 60 signatures to force an extraordinary meeting of the Ulster Unionist Council had been gathered and that party headquarters had accepted them as valid.
Amid some grass-roots anger at the disciplinary measures taken against Mr Peter Weir and Ms Pauline Armitage following their failure to support Mr Trimble in the Assembly vote for First Minister last week, some unionists are seeking clarity on decommissioning.
Anti-agreement unionists are keen to link participation in the Executive with progress on IRA decommissioning.