Unite ambulance staff have begun their second day of strike action.
As members of the union began striking yesterday in Wales, talk of a deal was described as "wholly premature".
But ambulance bosses have warned the service still faces "significant pressure" and have drafted in military personnel to drive ambulances.
The Welsh government said it would continue talks with Unite, who have further strikes planned for 20, 21 and 22 February.
Other health unions are set to ballot on a new pay offer from the Welsh government.
Eluned Morgan, Wales' Health Minister, said: "We're really pleased that all of the other unions have suspended their action.
"Obviously they now need to put that to their members and we really hope that they will take the opportunity to pick up this additional funding that has been really difficult for us to find.
"If they don't, its going to be made clear that there isn't anything else, there's no more money that we can find."
Adam Morgan is the senior negotiator at the Chartered Society of Physiotherapy in Wales, which postponed strike action planned for Tuesday.
He told BBC Radio Wales Breakfast on Tuesday: "We appreciate the difficult position the Welsh government are in with their budget.
"Unfortunately this doesn't go as far as we would like, however we think that in good faith from the negotiations we should pause it, to go to our members.
"We understand that there is no more negotiation on the amount of money available, especially for this year. We will be putting it to the members to decide whether they accept it and then its up to them to make their voice clear."
Mr Morgan said his union will be meeting the Welsh government on Tuesday for further talks with a view of consulting its members "in the next week or two".