Mr Albanese will continue to consult with Indigenous representatives after meeting with the Torres Strait Regional Authority on Thursday on top of local government and council heads from the Torres Strait and Cape York.
"I want to make sure that this is a successful referendum," Mr Albanese told the ABC on Friday.
"Yesterday, I received unanimous support for the voice to parliament, unanimous support for constitutional recognition for Aboriginal and Torres Strait Islander peoples."
The prime minister says the question to be put to the Australian people remains clear: Do you support First Nations people being recognised in our constitution with the voice to parliament?
The proposed change to the constitution outlines what the voice would be - namely an advisory body - and what it will not be, he said.
"It won't usurp the power of parliament, it will just be an advisory body on matters that directly affect Aboriginal and Torres Strait Islander peoples."
State and territory ministers have agreed to back the Labor government's work towards enshrining the voice in a referendum by the end of this term.
"They've all absolutely and enthusiastically committed to (the referendum," Indigenous Minister Linda Burney told the ABC.
"What was wonderful about that meeting is that we heard from each state and territory about their journey, about where they are with the implementation of truth, treaty and voice.
"I felt so enthusiastic after that meeting, and so positive because there really is a new dawn coming. I can feel it."
Ms Burney also took aim at the opposition's position about waiting for more detail before coming to a definitive conclusion.
"There is alot of detail already out there, they just have to read the Tom Calma, Marcia Langton report," she said.
"It's not like this is a new idea, it's been kicking around for decades and there is an enormous amount of information out there. The Uluru statement was so clear it would be an advisory body.
"At the end of the day, the shape and the role of the Voice will be determined by the parliament so they will have plenty of opportunity to have input into what it looks like, what its role will be."
It comes after Mr Albanese on Thursday said the voice would not lay the groundwork for financial reparations for Indigenous people.
"No, it won't. It's not about that at all," he said on Thursday Island.
"There's nothing in the proposed wording of proposed constitutional change that would alter that at all."
The Uluru Statement from the Heart calls for an enshrined voice and for the Makarrata Commission to "supervise a process of agreement-making between governments and First Nations and truth-telling about our history".
Mr Albanese's speech at the Garma festival in the Northern Territory last month laid out a proposed referendum question to enshrine an Indigenous voice to parliament in the constitution.
Mr Albanese is in the Torres Strait with Ms Burney and Queensland senator Nita Green, as part of a two-day trip for talks on what an Indigenous voice might look like.
