Members of Unite and the GMB will vote in the coming weeks on whether to launch a campaign of action following the failure of talks with the Offshore Contractors Association.
After the meeting, which involved the conciliation service Acas, the unions announced they will press ahead with preparations for official industrial action ballots.
Yorkshire has a considerable number of offshore workers based in the North Sea and further afield.
Unite regional officer Tommy Campbell said: "Unite members gave a significant mandate to hold a ballot for strike action in this dispute with the OCA employers.
"Offshore workers are gearing up to campaign for a yes vote. It is time for all union members to stand up now, and fight back for better terms and conditions."