Both sides of the voice campaign have pledged to unveil new measures to close the Indigenous disadvantage gap after the referendum failed.
Just under 40 per cent of Australians supported the Indigenous voice to parliament in Saturday's referendum.
The federal opposition has criticised Prime Minister Anthony Albanese for pursuing the referendum when polls showed it was heading for defeat.
They accused him of dividing the nation rather than pushing ahead with symbolic constitutional recognition without the advisory body, which they said they could have supported.
Opposition leader Peter Dutton said the prime minister had raised the hopes of Indigenous Australians through the voice referendum.
"He told them that he could deliver an outcome which he'd never had any capacity to deliver," he said.
"He sought to use the goodwill towards that (constitutional) recognition by masking the unpopularity of the voice.
But the prime minister rejected that, saying he had an obligation to Indigenous communities to fulfil the level of recognition they had called for.
"(The referendum) was not out of convenience, it was out of conviction," he told parliament on Monday.
"I believe that when you make a commitment, including a commitment to Indigenous people, it should be fulfilled.
"The referendum was about listening to people and about getting better outcomes, and these principles will continue to guide me."
Mr Albanese also hit out at the opposition leader backtracking on a pledge to hold a second referendum solely on constitutional recognition, should the coalition win the next election.
The prime minister said Mr Dutton was "all trailer, no movie", in response to the backdown.
Indigenous affairs minister Linda Burney said while she accepted the result, the pathway to closing the gap was not lost and she would unveil further measures to address disadvantage.
The coalition's Indigenous Australians spokeswoman Jacinta Nampijinpa Price will also begin crafting election policies to close the gap.
Senator Price went on the attack in parliament, pursuing the government over why it decided to go ahead with the referendum without splitting the question, meaning solely symbolic recognition did not get up despite multi-party support.
Foreign Minister Penny Wong said Labor had committed to taking the request by Aboriginal and Torres Strait Islanders to Australia.
"People should also respect the views of the many Aboriginal and Torres Strait Islander people who were part of that consultation process which led to the (Uluru) statement from the heart," she said.
Indigenous senator Lidia Thorpe - who spearheaded the progressive 'no' vote - said the government needed to focus on implementing the recommendations of a royal commission into deaths in custody.
The independent senator also pointed to recommendations from the Bringing them Home report, which outlined how to redress the impacts of forced removal policies and address the ongoing trauma people from the stolen generation face.
"Finally the dangerous distraction of the referendum is over and we can get back to the real fight," she said.
"Wake up, did the referendum not tell you we don't want some tokenistic gesture?
"We want real justice."
Former prime minister Scott Morrison said he felt for Indigenous Australians following the referendum, but said the voice was not the best model.
"The idea that this was somehow going to completely change their living standards, I think, is a cruel suggestion," he told Sky News on Monday.
"The Labor Party never offered us bipartisan support for a recognition model. Their condition was always that it must be the voice or nothing."
