Unison said it was suspending strike action scheduled for Monday to consult its 100,000 members north of the border on the revised offer from the Confederation of Scottish Local Authorities (COSLA).
The GMB and Unite were expected to follow suit.
In a statement, the union said that the improved deal offered by employers added a 0.5% increase to the previous offer, which prompted nationwide strike days in August and September.
Dougie Black, Unison regional officer and lead negotiator, said selective strike action scheduled would be cancelled so that members opinions could be sought.
“After two strikes and previous fruitless negotiations, I’m pleased that we now have a new offer,” he said.
“It is at a level - 3% this year and 2.5% for next year - that needs to go back to members to get their view. In the meantime we have agreed to suspend the selective action to allow this to happen.”
COSLA caused consternation among the joint local government trades unions after one round of negotiations last month.
Unison, the GMB and Unite all agreed to a new day of strike action when a mooted improved pay offer failed to materialise.