The union represents the majority of ambulance staff working for the NHS in Scotland.
GMB Scotland senior organiser for public service Keir Greenaway said the government's pay offer "doesn't go far enough" to help staff struggling with the cost of living crisis, or to improve the understaffing crisis affecting frontline services.
Mr Greenaway said the union wanted to get back round the table with Health Secretary Humza Yousaf before Christmas. He said: "It is important the cabinet secretary takes on board the views of all NHS staff and not just some, because we are talking about frontline workers who understand first-hand the crisis across service delivery and patient care, and they have clear and credible views on how these services can be recovered in the months and years ahead.
"The fact remains that GMB members in major services and health board areas have strong legal mandates for strikes and an imposition of this offer without further discussion would be seriously detrimental to the industrial relations the Scottish government have been quick to promote.
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