A previous vote had been in favour of a strike which would involve about 200 workers and would likely take place between August and October.
The Mariner field is due to start production in the second half of this year.
John Boland, UNITE regional officer for the North Sea, said: “There has been significant movement by Aker management over last week-end to address a number of the key concerns our membership have.
“These latest negotiations have been conducted in a constructive way.”
31 Jul 2018