Keeping Australia Day on January 26 has bipartisan support after Opposition Leader Bill Shorten ruled out changing the date, as Greens MPs threaten to bypass a government ruling by running their own citizenship ceremonies outside the public holiday.

"It will remain on the 26th of January," Mr Shorten said on Wednesday. "Having a national day is a good idea."

Bill Shorten with Indigenous Australian MPs Pat Dodson and Linda Burney. Credit:Alex Ellinghausen

The Labor leader pushed back against Prime Minister Scott Morrison's new dress code for citizenship ceremonies, which would prevent attendees from wearing board shorts or thongs.

"People want to be left alone on Australia Day. I don't want to be the fashion police telling people what they can wear at citizenship ceremonies."