Replace Queen's Birthday: NSW opposition

The NSW opposition leader says Australians should consider replacing the Queen's Birthday public holiday with a day to celebrate indigenous history as the Australia Day debate rages on.

Two Victorian councils have been stripped of the right to host citizenship ceremonies after they decided to cancel them on January 26 given many indigenous people view the date as "invasion day".

The move by the Melbourne councils has led the NSW Greens to back state councils considering taking a similar stance.

But NSW Opposition Leader Luke Foley isn't convinced Australia Day needs to moved from January 26, which is when the First Fleet arrived in 1788.

"I'm not in the business of rewriting history but there needs to be a completeness when we tell our history," Mr Foley told 2GB on Wednesday.

"Whether it's now or when Her Majesty passes away, whether that June public holiday would be best becoming the occasion, the public holiday where we recognise and celebrate 40,000-plus years of indigenous history here."

Lismore and Byron councils are considering moving celebrations from Australia Day.

"Decisions by local councils to hold citizenship ceremonies and celebrations on dates other than January 26 may be largely symbolic but symbols are powerful and create momentum for change," NSW Greens MP Dawn Walker said in a statement.

"Local councils have shown incredible leadership in passing motions in support of changing the date of Australia Day."