Australia Day next year will come two days late for one West Australian council.

The City of Fremantle has decided to move its traditional January 26 events to January 28 because of cultural sensitivities.

The council will celebrate One Day in Fremantle on January 28, with musicians such as John Butler, Dan Sultan and Mama Kin.

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The council describes the event as "an opportunity for all Australians to come together and celebrate the multicultural diversity of our country".

Mayor Brad Pettitt said the council was not opposed to celebrations on January 26, but was offering an opportunity for all Australians to come together on another day.

Dr Pettitt said the council had heard "loud and clear" from local Aboriginal elders that it was not a day to celebrate.

The announcement follows a growing push to move the national celebration to another day. (Source: AAP)

Australia Day marks the arrival of the First Fleet of ships from Britain in NSW on January 26, 1788.

Prime Minister Malcolm Turnbull told 3AW radio in Melbourne there was obviously some controversy about the date, as there was about most things, and to "stick with Australia Day on the 26th".

Former West Australian of the Year and former head of the Australia Day Council WA Robert Isaacs said it was divisive and concerning that a council was behaving contrary to what reconciliation was all about.

"Everyone around Australia has the opportunity to bring this nation together. Forget about the past and look at the good things," he told 6PR radio.

Local Fremantle business owner Jean Carlos Bello told AAP the move was "absolutely" sensitive to indigenous people.

There will still be a fireworks display on January 26 in Fremantle, but it will be funded by the Fishing Boat Harbour Traders Group and the Fremantle Business Improvement District.