Former Connaught workers staged a protest outside Hull City Council last week after contract complications led to wage payments being frozen.
The council transferred a maintenance contract and nearly 130 workers to Morgan Sindall subsidiary Lovell Partnerships following the collapse of social housing maintenance firm Connaught.
But the council reversed the decision in December, deciding instead to split the contract between Kier and Kingston Works.
Workers were being paid by Lovell until Wednesday last week, when payments were stopped.
Unions including GMB and Unison fear that staff have been abandoned while the contract transfer is completed and have threatened legal action.
The council said it was the firm’s responsibility to resolve the issue.
In a statement, Kier said: “Kier and KWL are in detailed dialogue with Hull City Council and will be liaising with trade unions in order to bring about a speedy and expedient resolution for everyone concerned.”
A spokesperson for Hull City Council said: “The council has not blocked any proposals for the transfer of staff between Lovell and Kier or KWL, and has advised the parties that they must take their own independent advice about TUPE. The council believes Kier and KWL are taking such advice.
“The council has been informed that Lovell have unilaterally decided to stop paying staff from midnight on 12 January, and that they are now employed by Kier and KWL; however, the council has received no official notification about this, and is urgently seeking further information to clarify the situation.”