Australians have turned out in their tens of thousands at Invasion Day protests across the country as a new theme emerges for the rallies.

Against the backdrop of long-running calls to change the date of Australia Day, many speakers were staunchly opposed to an Indigenous voice to parliament despite key Aboriginal and Torres Strait Islander figures backing the proposal.

Canberra’s Garema Place was packed with people opposed to the national day as well as the voice to parliament, the public square littered with posters reading “f*** your voice – manufactured constitutional consent”.

Crowds around the nation demanded land rights and an end to deaths in custody, while calling for the national day to be abolished as January 26 marks the start of British colonisation.

Many speakers called for treaty before constitutional recognition, one describing truth-telling as “the spear in the leg Australia needs”.

The ACT protesters marched through town to the Aboriginal Tent Embassy, below Old Parliament House, to cries of “no pride in genocide”.

Ngambri and Ngunnawal woman Leah House labelled the proposed voice as “crumbs”, “f***ing uncompelling”, “vague” and “a distraction from what our ancestors and elders have been fighting for”.

“Why the f*** would we accept our political role in this country as an advisory body?” she asked.

“That’s inconsistent with our sovereignty, to accept a role as an advisory body, not as a decision-maker.”

Ngunnawal woman Nioka Coe, whose father was a founding member of the Aboriginal Tent Embassy, said constitutional recognition “will silence our people”, while blasting government officials for not “sitting at the campfire and discussing our terms”.

“Our people go back more than 5000 generations in this country, we are sovereign people … we never relinquished our right to this country, we are the survivors of the atrocities committed against our people,” she told the crowd.

At Sydney’s Belmore Park, Wiradjuri woman Lynda-June Coe told the thousands-strong crowd the proposed voice was a “fallacy”.

“White Australia, this is the reckoning – 235 years and we ain’t going nowhere,” she said.

“They tried to wipe us out, still here. They tried to breed us out, still here. They tried to commit genocide on us, still here.”

Several speakers at a rally through the Melbourne city centre spoke out against the voice, although organisers stressed the rally did not specifically endorse a “no” campaign.

Aboriginal activist Gary Foley said people had to be careful not to be sucked into a measure that would ultimately be “lipstick on a pig” and said there wasn’t a “snowball’s chance in hell” a referendum would pass.

“The Australian parliament today is not interested in listening to the voice of Aboriginal people … why should we expect that yet another advisory body (would)?” he said.

Indigenous academic Tom Calma, the newly appointed Senior Australian of the Year and a campaigner for the referendum on the voice, said the issues facing Indigenous people and the need to step towards reconciliation could co-exist.

“It’s important that we as Aboriginal people have an opportunity to be able to contribute to policies that impact on us and programs and legislation and that’s the first step,” he told ABC Radio.

By Alex Mitchell, Phoebe Loomes and Rachael Ward in Canberra