A West Australian shire council has voted not to fly the Aboriginal flag outside its offices during NAIDOC Week, with its president saying it would be divisive to do so.

Carnarvon Shire Council president Karl Brandenburg cast the deciding vote in a favour of not flying the flag when the poll earlier this week ended in a tie.

NAIDOC Week runs from July 3 to 10 and celebrates Aboriginal and Torres Strait Islander history, culture and achievements, and recognises Indigenous Australians' contributions to the country.

Cr Brandenburg told 720 ABC Perth he believed flying the flag would be divisive, not inclusive, and said the Australian flag represented all nationalities of the local community.

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"From my point of view I've got to take citizenship ceremonies in there quite regularly ... I think it's only fair that [different nationalities] should do it under the Australian flag," he said.

Cr Brandenburg said while he was "respectful of the Aboriginal communities", the fact it was NAIDOC Week did not change his thinking.

"The NAIDOC flag can be flown at their buildings or buildings where they're having events and all those areas," he said.

"The shire offices are not where they're holding the event, so they need they need to understand and reflect the fact that we are one nation and we are all Australian, and that's what citizenship's under.

"What do I do next, have a sporting club come and say 'we've got a big sporting event, I want to raise our flag'?"

Indigenous leaders condemn decision

The request to fly the Aboriginal flag above council headquarters was lodged by NAIDOC committee member Susan Oakley.

"I'm upset and angry ... it's important for us because we are the first people of this nation," she said.

Critics say the council's decision not to fly the Aboriginal flag is a poor one. ( Getty Images: Ian Waldie )

"If they don't recognise us as a people then what hope is there for us in Carnarvon to have reconciliation with them?"

The criticism was echoed by other Indigenous leaders and politicians, including Carnarvon Yamatji woman Evelyn Ronan.

"I'm totally disheartened at the moment to hear such a foolish statement made by our shire president," she said.

"Seeing our flag flying during NAIDOC reminds me of our past and how far we've travelled, and it makes you want to be a proud Australian ... Indigenous people should be made to feel proud of ourselves."

Head of Edith Cowan University's Kurongkurl Katitjin Centre for Indigenous Education and Research, Colleen Hayward, said she was disappointed.

"The Aboriginal flag is registered, it is recognised by the Australian Government as an official flag of Australia," she said.

"Probably lots of people are thinking that there is a single Australian flag, and in fact there is not.

"I don't think the councillors at the Shire of Carnarvon have thought through this enough."

'A load of rubbish', local MP Catania says

WA Nationals MP for the North West Vince Catania said the decision was misguided.

"This is not a reflection of the Carnarvon community, this is not a total reflection of all the councillors on the Shire of Carnarvon," he said.

"To say you need to have an Australian flag fly solely is a load of rubbish.

"They should be flying the flag. Given the fact that 20 per cent of our population is Aboriginal, [they] should be flying every day throughout the year."

Labor MP for Victoria Park Ben Wyatt tweeted that the first task for the day was to send the council an Aboriginal flag.