David Trimble is expected to attempt re-election on Friday
After meeting at the weekend, the Ulster Unionist Party executive agreed to call on the party's 28 assembly members to back Mr Trimble's return to office following the IRA's move on decommissioning.
However, the party leadership's decision to support a return to powersharing with Sinn Fein could be thwarted if dissident Ulster Unionist assembly members oppose it.
On Monday, Ulster Unionist assembly member Pauline Armitage said at present she did not feel inclined to support David Trimble for re-election as first minister.
She said she was not happy with the direction the party was taking and that her questions about IRA decommissioning had not been answered.
"I would have no pleasure in voting against the leader of the Ulster Unionist Party," she added.
"I am committed to the party and I believe in the party. But unfortunately I feel I have no more role to play in the present Ulster Unionist Party."
Another Ulster Unionist, north Down assembly member Peter Weir, has also criticised the IRA move as "a one-off stunt".
Mr Weir said on Monday he would wait to the "last minute" before giving a decision on whether or not to back Mr Trimble.
"Right now, I don't think the information is there to enable anyone to vote in favour of any first minister, but we will have to wait and see what information develops over the next few days," he said.
Mr Weir is seeking a meeting with the head of the arms body, General John de Chastelain, to get clarification over IRA decommissioning.
Ruling council meeting
Meanwhile, Hardline UUP members have collected the signatures necessary to call for a meeting of the party's 860 member ruling body, the Ulster Unionist Council to discuss a return to powersharing and alternatives.
Party rules dictate that Ulster Unionist Party officers must fix a date for a council meeting within 21 days after it is requested.
David Trimble has consistently won backing for his policies at recent UUC meetings, but by an increasingly narrow margin.
However, it is expected that an election to the Northern Ireland first and deputy first ministers posts will be held before that on Friday.
To be re-elected as first minister along with the nationalist SDLP's Mark Durkan as deputy first minister, Mr Trimble will have to gain a majority of support within both the unionist and nationalist blocs in the assembly.
He resigned in July because of an absence of IRA decommissioning and then pulled his ministers out of the Northern Ireland Executive two weeks ago to put further pressure on republicans.
'Concessions'
Despite the IRA move, the anti-Good Friday Agreement Democratic Unionist Party has warned Mr Trimble his election is not assured.
DUP assembly member Ian Paisley junior said he expected a collapse in the power-sharing arrangement to trigger a full assembly election.
The Women's Coalition said on Monday its two members were prepared to re-designate themselves as unionists to ensure Mr Trimble succeeded.
They sit in the assembly as "others".
Assembly member Jane Morrice said the aim of re-designation would be to protect the Good Friday Agreement.
"It is a genuine attempt to keep this peace process alive," she said.
She and party colleague Monica McWilliams introduced a motion to the assembly asking for the 30-day notice required for re-designation to be waived.
Members of Sinn Fein's Ard Comhairle met in Navan in County Meath on Monday night and passed a unanimous motion commending the IRA for its decision to decommission some of its weapons.
Part president Gerry Adams said: "The last week has been a hurtful one for many republicans trying to come to terms with decommissioning. We thought we should meet nationally to discuss the situation.
"Clearly the response from people everywhere is an emotional one. Even those who can rationalise and see the logic and support what is happening are hurting very, very much."
Meanwhile, Billy Hutchinson, one of two loyalist Progressive Unionist Party assembly members, said his party would decide this week whether to support David Trimble in his attempt to be re-elected as first minister.
Mr Hutchinson said the PUP had concerns about the future of the Agreement because too many concessions were being given to republicans.