Canberra: Politicians are continuing to debate Australia Day, which was named during the 1930s but only given a permanent date for commemoration in 1994, and remains a fraught issue.

The Greens leader, Richard Di Natale, sparked the latest round of controversy when he told the Australian his party would campaign to have Australia Day, which is now 26 January — a day that marks the 1788 arrival of the First Fleet and the colonisation of Australia — changed.

The “change the date” campaign has grown in prominence in recent years. Some Indigenous leaders and other Australians have long referred to 26 January as Invasion Day, and held marches and other commemorations of the loss of life, land and culture among Aboriginal and Torres Strait Islander people since colonisation.

States and territories adopted the term Australia Day for commemorations of federation in the 1930s. Australia Day was gazetted as a public holiday in the 1940s but the date shifted each year to ensure a long weekend. For the 1988 bicentennial celebrations it was agreed 26 January would mark Australia Day that year but it wasn’t until 1994 that it was established as a fixed date.

Last year, councils in Fremantle, Yarra and Darebin, which all feature Greens representatives, voted to shift their citizenship ceremonies and Australia Day celebrations to another day, which led to a swift and hostile response from the Turnbull government. Inspired by the councils, Di Natale said his party would move to shift the date permanently.

The deputy prime minister, Barnaby Joyce, immediately dismissed the Greens’ push.

“We are building inland rail systems, they’re talking about Australia Day,” he said at a press conference in Parkes on Monday. “They think that Lachlan Macquarie and Captain Cook were bad buggers.

“I am completely at ease with Australia Day. I’m very proud of Australia Day, and it is what you make it. We take into account every person who makes up this great nation, the Aboriginal people ... Torres Strait Islanders, people who have come from England, Ireland, Scotland, Wales, Greece, Italy, China, Japan, the Arctic Circle. I don’t care, wherever you’ve come from, you’ve come to this nation and this nation is now your home.”

Labor does not have an official policy on the move — Bill Shorten’s office pointed to the statement the opposition leader made in parliament in August, following the Turnbull government’s attack on councils that announced date changes to their Australia Day ceremonies, in which he said he did not support a date change.

But others within the party said there was need for conversation and a potential date change.

“Out of respect for Indigenous Australians and as a proud descendant of Irish convicts I don’t think Australia Day should be 26 January which marked the foundation of a penal colony,” the Shortland MP, Pat Conroy, said.

“I would support Australia Day being moved to a day that commemorates when Australia truly became a nation, such as a key date in the Pacific WWII campaign or the 1967 referendum.”

The Queensland senator Murray Watt also said he would be open to changing the date.

“I think we should celebrate our national holiday at a time that does not cause hurt to our First Australians,” he said.

“Any change would need consultation with all Australians, but I think it should be a date that celebrates a confident, diverse and united Australia. An Australian Republic Day would be ideal.”

The Victorian MP Andrew Giles said more work needed to be done to make “citizenship more inclusive”.

“This requires discussing what it means to be Australian,” he said. “We are big enough as a nation to find ways to give everyone’s story space in our Australian story, and of course to complete our journey to reconciliation with First Nations peoples.”

Triple J, which had mostly hosted its annual Hottest 100 countdown on 26 January since 1998, announced in November last year it was moving the event to the fourth weekend in January, after a listener survey showed the majority wanted the date changed.