Unite and the RMT union are representing about 350 workers involved in a dispute over pay and conditions with oil services company Wood Group.
Some workers claim they are facing cuts of up to 30%. Wood Group denies this.
The Aberdeen-based firm provides maintenance and construction to Shell and signed a three-year extension to its contract earlier this year.
Unite said the unions offered to suspend industrial action if Wood Group removed the current proposal for changes to pay and conditions in full, to allow further talks.