About 46% will vote yes to having the new advisory body, called the Indigenous "Voice to Parliament", while 43% would vote no, according to the Newspoll survey published in the Australian newspaper on Monday.
The poll comes just days after the referendum legislation cleared its first parliamentary hurdle as it was passed in the House of Representatives.
This is the first survey to poll voters on the precise question they will be asked at the ballot box when the referendum is held, expected between October and December.
Another poll last month found the yes vote dipping to 53% from 58% earlier this year.
While a majority of Indigenous people support the Voice, others argue it is a distraction from achieving practical and positive outcomes.
Persons:
Read, Anthony Albanese, Praveen Menon, Ediring, Michael Perry
Organizations:
Australian, Torres Strait, Thomson
Locations:
Rio Tinto, Perth, Australia, SYDNEY, Australia's