Dexter said Thursday he wouldn't reveal that information because the union representing the workers hadn't ratified the agreement and he didn't want to influence the arbitration process, should it be accepted.
"It would be my preference to wait until the arbitrator rules because why would I speculate about what the cost would be if I don't know," Dexter said at the legislature.
"That to me seems not to be a responsible position."
If the union membership accepts the deal from the Capital District Health Authority, a board of arbitration would have to come up with pay increases that range between 6.5 per cent and nine per cent over three years.
The contract says a final decision should be made by June 15. A vote by members of the Nova Scotia Government and General Employees Union was expected to wrap up Friday.
Opposition Liberal Leader Stephen McNeil said the public has the right to know what the deal could cost.
McNeil added that he believes the government already knows what costs it could be facing should the arbitrator award either the minimum or maximum amount under the deal.
"The premier should be telling the taxpayers of Nova Scotia what they potentially could be on the hook for and making sure that we have a full debate about it," said McNeil.
He also criticized Dexter's reluctance to say whether the contract would be paid for by the health district or the government's budget.
"Surely he is not going to ask districts to absorb this cost when they have been given their budgets already," he said.
Progressive Conservative Leader Jamie Baillie said the cost should be a matter of public record because it will have ripple effects for public service negotiations to come.
"We know that whatever the final number is here, it's going to be multiplied over and over again across all of the other government unions," said Baillie.
He said now that negotiations have concluded, it was time for the government to consider passing essential services legislation in order to prevent disruptions to the health system such as the surgery cancellations and bed closures that came in anticipation of a strike.
Dexter said the government would assess its position on the issue after the union finishes its vote.
"My focus at this time though is not on anything like that," he said. "It is on resolving the current situation, getting an agreement and making sure that public services are fully restored."
Members of the union work in over 250 different roles, including lab technicians, social workers, occupational therapists and nurses.
The union had been asking for a wage increase of 5.1 per cent to match a raise given to some nurses last year.
That arbitrated award effectively broke a government template of offering increases of one per cent in each of two years to public sector unions.