The Alliance Party is refusing to back the Ulster Unionists for any top posts on Belfast City Council because of its links with the Progressive Unionists.
The Alliance Party holds the balance of power on the council
The Alliance holds the balance of power on the council, and its councillors will support the SDLP's candidate for city mayor in the election on Thursday.
The UUP have come under pressure over their assembly arrangement with the PUP, which has links with the UVF.
Naomi Long of the Alliance said all loyalist groups must be on ceasefire.
"We have made it clear that whilst the UUP maintain their formal links with the PUP and the UPRG, and whilst the paramilitary groups to which they are linked are not on ceasefire and refuse to address decommissioning, Alliance will not be in a position to support them for any of the top posts," she said.
"Unlike others, we will not differentiate between loyalist and republican paramilitarism, but want to see all groups commit to exclusively democratic and peaceful means and move towards a peaceful and shared future."
As the assembly reconvened on 15 May, Progressive Unionist Party leader David Ervine joined the Ulster Unionist grouping.
The move would give the UUP an extra ministerial seat at Sinn Fein's expense if a power-sharing executive is formed.
Sylvia Hermon, the party's only MP, was among those who have criticised the move.
And the party has come under renewed pressure following Tuesday's shooting of Mark Haddock, who was named in a court case as being a leading member of the Ulster Volunteer Force.
However, party leader Sir Reg Empey said on Wednesday he was trying to help stop such attacks.
"We have a political arrangement with one MLA and that does, of course, have negative things with it," he said.
"But there is also a longer-term commitment I have made. I am prepared to give it a real try."