Members of the Northern Territory's Country Liberal Party (CLP) have voted to back the 'No campaign' in the upcoming referendum on an Indigenous Voice to Parliament.

The move has been welcomed by the CLP's sole federal representative, Senator Jacinta Nampijinpa Price.

But it is not yet clear what the rebuke will mean for the CLP's parliamentary leader, Lia Finocchiaro, who last week said she supported the Voice in theory but held concerns about a lack of detail from the federal Labor government.

At a closed-door Central Council meeting south of Darwin on Saturday, party delegates reportedly voted in favour of several motions to oppose the Voice, meaning it will now become the official party position.

It comes after Senator Price, who has been critical of the Voice to Parliament concept, earlier this month said the party would fall into line behind her.

A referendum on First Nations recognition in the constitution will be held in the second half of this year.

Federal and Territory Labor are backing the Yes vote, while the federal National Party have openly backed the No campaign.

Liberal leader Peter Dutton has not outlined his position. 

In a statement released late on Saturday, Senator Price said she applauded the Central Council for backing her stance. 

"The CLP has sent a clear message that it will fight for an Australia in which all Australians are equal and these motions reflect that," she said.

"Australians do not want racial division written indelibly in our Constitution.

"The Voice is divisive, it is a dangerous threat to our democracy and it is unfair. I am grateful to the members of the CLP who voted to oppose it."