Post Office workers in Witney and Carterton have called off their strike scheduled for Thursday and Friday.
But a spokesman for the Communication Workers Union (CWU) Bob Cullen warned that members could still go ahead with the threatened official strike as early as next week if they rejected peace proposals at a mass meeting called for tomorrow night.
However, he said: "I am confident that members will accept the proposals. We have achieved more than an apology from management over the issue of bullying, but I cannot go into details before the meeting."
If members reject the proposals hammmered out between union and management, the union will again give the statutory seven days' notice of its intention to strike.
Members called for a series of official strikes after alleged bullying incidents which the union said resulted in several members staying off work due to stress.
At the beginning of July, workers at the two depots took wildcat strike action which resulted in a backlog of mail to be sorted.
At the start of September, they took three days of official strike action which delayed mail deliveries in west Oxfordshire by up to a week.
Royal Mail spokesman Sue Dakin said: "If it is true that the union has decided not to take action this week then we are very pleased that common sense has prevailed, not least in the interests of our customers and the maintenance of their services.
"We remain committed to building better relationships in the units at Witney and Carterton and work has been on-going to achieve this in recent weeks."
Staff at a Ministry of Defence base in Bicester earmarked for closure are waiting to hear the results of their ballot on industrial action.
The Prospect Union asked its 104 members at the Defence Logistics Organisation in Caversfield to support working to rule in a ballot which closed on Friday.
Results are now being counted. The Prospect Union is opposing plans to relocate the base to Bristol, putting up to 240 jobs at risk.
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