A row has broken out over PUP leader David Ervine joining the Ulster Unionist assembly grouping.
David Ervine has joined the Ulster Unionist group at the assembly
Ulster Unionist leader Sir Reg Empey said the move would cost Sinn Fein a ministerial seat.
"A unionist executive would reflect a unionist majority," he said. Assembly speaker Eileen Bell will rule on the move on Tuesday.
DUP leader Ian Paisley said by linking with the PUP the UUP were "allying" themselves with terrorism.
The party's deputy leader Peter Robinson said the Ulster Volunteer Force - with which the PUP has links - was active in criminal and paramilitary areas, according to the latest report by the Independent Monitoring Commission.
"That is a very clear issue," he said.
"One that we see not as a pragmatic matter but as a matter of principle."
Mr Robinson queried the move in the assembly chamber when it met on Monday.
Ms Bell said she would take counsel before ruling on it.
Speaking outside the chamber Mr Paisley said that his party would "have nothing to do with terrorism".
"If people want to be allied with any form of terrorism whether it be Protestant or Roman Catholic or something else they have no right in the government here," he said.
Mr Ervine said that a stronger unionist presence on any executive that was formed would bolster confidence in his community.
"I think I'm doing a very logical, shrewd political move," he said.
"One that perhaps people should have thought of long ago, that if you move across to bolster your own community - unionism - that our community will then have greater confidence in moving on to what is the next phase of the peace process."
The UUP said the move would pass a third Sinn Fein executive place to them and see a unionist majority for the first time on the executive.