More than 7000 polling places are receiving voters on Saturday and will continue to collect ballots until 6pm.
Voting began as the latest Newspoll showed the voice proposal is set to fail and, despite a late swing towards a 'yes' vote, may fall short of securing a majority in any state.
Making his final pitch to voters in Sydney on Saturday Mr Albanese said he had done everything he could to campaign strongly for a 'yes' vote.
"I am very hopeful of a 'yes' vote this evening," he told reporters.
"I stand here before you today as the 31st prime minister of Australia, saying this is an opportunity for Australia to unite, to be strengthened by reaching out to our most vulnerable citizens."
In an opinion piece released early on Saturday Mr Albanese said the referendum was a chance for Australians to "get it right" and show "a generosity of spirit".
"Rather than listening to the people who could guide them towards the best results, governments of all persuasions have wasted billions in a muddle of good intentions that haven't gotten results," he said.
Voters are being asked to write 'yes' or 'no' to recognise the first peoples of Australia by establishing an Aboriginal and Torres Strait Islander voice in the nation's founding document.
A Newspoll survey published in The Weekend Australian shows a three-point swing toward a Yes vote over the past week to 37 per cent.
With 57 per cent of surveyed voters saying they intended to vote 'no' as of Friday, a point down on the previous poll, the referendum would be lost if the poll results were reflected at the ballot box.
Six per cent of voters said they remained undecided.
If their votes were split equally to both sides of the debate the final result would be 60-40 against the voice.
Newspoll found there was not a single state where the 'yes' vote was ahead of the 'no' vote.
Opposition Leader Peter Dutton said a simple change to the constitution recognising Indigenous people would have received almost unanimous national support and been a "unifying moment" for the nation.
"I think most Australians, particularly when we don't have the detail about how it would work, are going to vote 'no'," he said.
When asked about the polls showing a victory for the 'no' vote, Minister for Indigenous Australians Linda Burney told the ABC she would work till close of polling on Saturday to convince people to vote for a better nation.
"This was a generous request from Aboriginal and Torres Strait Islander people. This referendum and a 'yes' vote will not affect most people's lives but it will mean so much to Aboriginal and Torres Strait Islanders," she said.
Nationals leader David Littleproud told the ABC that the prime minister had divided the country and healing would now need to take place.
"If this referendum was about constitutional recognition and that alone, we would have supported it. That would have been a unifying moment," he said.
"In terms of the result, no one should feel guilty about how they vote today or guilt about the result."
As of Friday, five million Australians had already voted out of 17.7 million enrolled electors.
Postal votes can be received up to 13 days after the referendum but Australians must complete these by 6pm on Saturday.
