Labor’s $160m plan to ask Australians to vote “yes” or “no” to becoming a republic has been met with strong criticism from Indigenous people campaigning for constitutional change to recognise first peoples.

Labor announced on the weekend that, if elected, it will commit to holding a public ballot on the republic in its first term of government.

“We’re not saying it’s the most important issue but we are saying that, if we are elected, it’s one of the issues that Labor will attempt to deal with during our first term,” Labor’s spokesman on the issue, Matt Thistlethwaite, told Fairfax Media.

The Northern Territory branch secretary of the Maritime Union of Australia and president of the NT Trades & Labour Council, Thomas Mayor, was part of the Uluru convention and has been touring the country ever since, helping build support for the Uluru Statement from the Heart.

“We’ve just had this amazing moment [with the Uluru statement], we’ve been pushing it, and we’re going to get sent to the back of the bus to wait for a republic that does nothing to empower our people,” he said.

Speaking at the Griffith University Centre for Governance and Public Policy in Brisbane on Tuesday, Mayor said that any movement for a republic must wait until progress has been made on reconciliation.

Thomas Mayor says reconciliation is ‘the most important constitutional reform’. Photograph: Carly Earl/The Guardian

“This people’s movement needs to respond to that and say no,” he said. “Achieve reconciliation first. That is the most important constitutional reform right now. We’re not going to go to the back of the bus.

“I’d be prepared to organise to see a republic plebiscite go down, because it’s a real slap in the face without a first nations voice coming first.”

The national director of the Australian Republican Movement, Michael Cooney, said Labor’s announcement was welcome but it was not the only important constitutional question.

Cooney said the ARM supported the Uluru Statement from the Heart and “Australia should have a national vote on the Indigenous questions on the date and in the form that Indigenous leadership and community want it held”.

“It’s not so much a matter of who goes first, as what happens when,” Cooney said. “Labor’s timetable for a republic vote by 2022 is welcome but Labor should also articulate a timetable on responding to Uluru.”

• Additional reporting by Ben Smee