The largest civil service union, the CPSU, has voted in favour of the Landsdowne Road agreement.
Members voted to accept the deal on public service pay and conditions by two-to-one.
The Irish Federation of University Teachers have also voted to accept the deal.
However, three-quarters of Unite trade union have voted to reject the proposals.
It comes ahead of a meeting of public sector unions on Wednesday, when an overall vote will be held.
Commenting on the outcome, CPSU general-secretary Eoin Ronayne said the union saw the Landsdowne Road agreement "as just a start on the road to the full restoration of all pay and conditions cut since 2008".
Welcoming the result, he said: "The members recognised that the flat rate mechanism used to restore some of the pension levy and basic pay in the deal prioritised lower paid workers".
But he added that the failure of the Government to put more than €270m a year on the table meant many long serving lower income public servants at the top of their scales felt aggrieved.