Scott Morrison has emphatically rejected introducing an indigenous voice to parliament, claiming it would be nothing more than a "third chamber" of power.

The prime minister is not mincing his words on a constitutionally-enshrined representative body for indigenous people, as recommended by the Uluru Statement from the Heart.

"I don't support a third chamber," he told ABC radio on Wednesday.

This characterisation has been roundly rejected by First Nations people.

When pressed on the fact the voice to parliament would not be a third chamber, he replied: "People can dress it up any way they like, but I think two chambers is enough."

"The implications of how this works frankly lead to those same conclusions, and I share the view that I don't think that's a workable proposal," Mr Morrison said.

The prime minister said he was passionate about reconciliation.

"But that doesn't mean we have to agree on every proposal, but every proposal will be treated with respect and we will find a way forward."

Indigenous Labor representatives Pat Dodson, Warren Snowdon and Malarndirri McCarthy said they were disappointed but not surprised by the prime minister's response.

"After all, this is the same government that repeatedly and disrespectfully dismisses and mischaracterises the aspirations of First Nations people," they said in a joint statement.

"Only Labor is committed to meaningful recognition and reconciliation through a constitutionally enshrined voice to parliament and a national process of truth-telling and agreement-making."

Mr Morrison also back-pedalled on his idea for a new national day to celebrate indigenous people and culture.

He floated the proposal this week and reignited debate on keeping the Australia Day public holiday on January 26.

"I haven't said it's a public holiday or not a public holiday, I haven't been so specific, I just think we should have a chat about it," he said.

Mr Morrison said he wanted to celebrate the achievements of Aboriginal and Torres Strait Islander people, but would not be changing Australia Day's date.

In arguing his point, the prime minister again pointed out the ACT holds a public holiday on May 28 to mark the anniversary of the successful 1967 indigenous referendum.

He also noted the annual NAIDOC week celebrations.

"Are we doing something which sufficiently acknowledges the great contribution and success of our indigenous peoples?"