While they are still open to negotiations, they say they have not ruled out industrial action.
Later this week Mr Parker will speak with other public sector workers, after sending a letter saying "there is no more money" to pay them more than what he has already offered.
However, Prospect, the local civil servant union who also rejected the August pay offer, says it doesn't believe there is no more money.
Next week it is going to ballot its members on potential strike action..
Both the States and civil service union think they are unlikely to reach an agreement.