The civil servants intended to strike later in the week over a 2.5% pay deal, but their employers have suggested an improvement on this offer.
Dougie Black, Scottish organiser at trade union Unison, said: "After two strikes and previous fruitless negotiations, I'm pleased we now have an offer.
"It is at a level - 3% this year and 2.5% for next year - that needs to go back to members for their view. In the meantime we have agreed to suspend the selective action to allow this to happen."
Signs of breakthrough in Scottish local government pay dispute
Scottish local government employees have suspended a third day of strike action to consider a new pay offer.
