Yesterday, eight firms of the 44 found to be using blacklisted workers announced they are working together to develop a scheme to compensate construction workers whose names were on the secret blacklist.
Unite is calling on the remaining 36 firms not to "shirk their responsibilities" and commit to joining the scheme "without delay".
The union said getting blacklisted workers back into employment "must be a priority".
Since the blacklist was discovered in 2009, following an investigation by the Information Commissioner's Office (ICO), workers have claimed they have been denied work because they were active members of a trade union group or for raising legitimate concerns about health and safety on building sites.
Gail Cartmail, Unite general secretary, said: "The fact that only eight of the 44 construction firms involved in blacklisting have committed to action is not good enough.
"Thousands of construction workers have had their lives, and the lives of their families, destroyed just because they belonged to a trade union or raised concerns about health and safety in one of the most dangerous industries.
"It must now be a priority to get blacklisted workers back into work.
She added: "Many of these workers have spent years out-of-work as a result of being blacklisted. Employers have a moral duty to give them back the jobs that were wrongly taken away from them."
In a joint statement the eight companies that agreed to offer compensation said they "apologise for their involvement and the impact it has had on any construction worker".
They said they would support the introduction of a code of conduct to ensure "nothing like this happens again".
