Hopes of averting further disruption of council services rose even though unions have set two further dates for one-day strikes.
Council workers will walk out on August 14 and again in September in a dispute over pay after this week's first national walkout in 23 years.
The action by thousands of workers in Sussex caused chaos with schools, leisure facilities, libraries and museums all forced to shut.
But their employers have now opened the door to negotiations after indicating a two or three-year pay deal could be discussed if talks restarted.
Unions said they welcomed the movement and urged employers to start serious talks They have called for a six per cent increase but have only been offered three.
A strike which threatened to stop supplies to Shell petrol stations was called off today after a last-minute pay deal.
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