Nearly three-quarters of staff who voted on the offer from their bosses at the Australian Institute of Aboriginal and Torres Strait Islander Studies said no to the proposed agreement.

It was the first offered since their last agreement ended in mid-2014, and staff last received a pay rise the year before.

The main public sector union blamed AIATSIS bosses for the rejection, saying they had insisted "on stripping critical consultation and representative rights from the agreement", but the agency said it had kept forums for consultation in the deal.

Community and Public Sector Union deputy national president Rupert Evans said staff were still prepared to stand up for their right to consultation and representation at work.

"AIATSIS staff shouldn’t have to, and won’t, accept a lesser deal than what other agencies have agreed," he said.

"There’s a clear path forward here – management need to respect staff, drop the attacks on key workplace rights and reach a sensible settlement."

AIATSIS was already at the lower end of public service pay scales, the union said.

Those in the the lowest-paid APS 1 band received a pay increase in 2013 taking them to just short of $40,000 a year. A mid-ranking APS 6 staff member saw their salaries go to $72,000.

Mr Evans said the agency's managers offered staff a cut to real wages with a pay offer of 3 per cent on commencement, then 2 per cent, and later 1 per cent over the three-year agreement, failing to recognise that staff had to wait several years for the agency to table an offer.

AIATSIS, which employs 140 public servants, said it offered staff a 6 per cent pay rise expedited over 18 months.

"We are committed to continue to work with staff in relation to the enterprise agreement and remain hopeful to see an agreed outcome in the future," the agency said.