Indigenous Australians Minister Linda Burney has accused Peter Dutton of “bully boy tactics”, as she outlined her hopes for the Indigenous Voice to Parliament.

It came after the Opposition Leader urged Ms Burney “to be honest” about the Voice, and claimed that Prime Minister Anthony Albanese’s “obsession” with it was fuelling Australia’s cost-of-living crisis.

In a wide-ranging speech to the National Press Club in Canberra on Wednesday, Ms Burney said if this year’s referendum was successful, the Voice would be asked to give advice on four key policy areas – health, education, jobs and housing.

“People are worried about their children’s future, about education, about jobs, about medical services and there hasn’t been one community that I haven’t visited that hasn’t raised the issue of housing,” she said.

“Josie Douglas, who is a wonderful Australian from the Central Land Council, put it best; the Voice will be changing lives, not changing public holidays.”

Ms Burney went off-script during her speech, to take aim at the “no” campaign, accusing it of bringing “Trump-style politics” to Australia.

“It is post-truth and its aim is to polarise, to sow division in our society by making false claims, including [that] providing advice to government would somehow impact the fundamental democratic principle of one vote, one value,” she said.

“Do not let the ‘no’ campaign get their way with using Trump-style politics in Australia. Do not let them divide us. The proposed change is constitutionally sound and legally safe.”

Asked about rising tensions between proponents of the yes and no sides, and if they might last beyond the referendum, Ms Burney said she had faith in Australians.

“I have a very deep commitment and a very deep view that Australians will rise to this. I have every faith, and when we think that it’s going to be about practical outcomes and recognition, there is nothing to fear in what’s being proposed,” she said.

“We are very conscious of the issues around mental health and just where this debate could go. We’ve already seen some fairly unsavoury things.

“But I say these things to you, that the ‘yes’ campaign is going to be positive, it is going to be respectful and it is going to be absolutely about the issues that affect First Nations people. It will not be about sowing division.”

Her comments about Mr Dutton came after he lashed Australian mining giants and other big companies for donating to the “yes” campaign. On Sunday, he said many big companies “lacked a significant backbone” on the upcoming referendum.

“There are a lot of people who are just craving popularity and are trying to please people in the Twittersphere,” he told Sky News on Sunday.

On Wednesday, Ms Burney – a Wiradjuri woman – said business support for the Voice was not new.

“It is the business community that supports the Voice, because they know that it is about employment. It is about making sure that people stay in jobs. It is very much what they are driving through their businesses,” she said.

“And I don’t think the business community would be very impressed by the bully boy tactics of Peter Dutton.”

Earlier on Wednesday, Mr Dutton said he had no regrets about his comments. He also tried to draw a link between cost-of-living pressures and the Voice.

“I think the fact is [that] many of the listed companies in Australia today, the CEOs are worried about … the Twittersphere, and they’re less worried about what’s happening to their customer base,” he said.

“I think for a company, for example to look at Wesfarmers, I think their $2 million would be better off [spent] reducing prices in their supermarkets.”

Mr Dutton said Mr Albanese had an “obsession with the Voice” that was distracting him from economic policy.

“That’s why you’re paying more for your mortgage, it’s why you’re paying more for every element in your family and small business budget. And yet inflation is sticky, it’s nowhere near the 2-3 per cent target range the Reserve Bank governor has in mind,” he said.

He said the Voice would change Australia’s system of government, without delivering practical change for Indigenous Australians.

“That’s why I think Linda Burney today needs to be honest instead of trying to pull the wool over the eyes of the Australian public,” Mr Dutton said.

He said there was no disputing Ms Burney wanted to help Indigenous Australians – “we all want to do that”.

“But the problem is that it goes much further than what she’s suggesting today, and this continuous misleading of the Australian public by Minister Burney is only making a bad situation worse for the yes case,” he said.

In response, Ms Burney told the NPC she believed that Australians would “come to understand” that the Voice was two simple propositions – recognition and practical outcomes.

“People need to understand that misinformation and disinformation is damaging, and I do not apologise [for that view],” she said.

The referendum’s success depends on majority support across the country and in four of six Australian states. It must be held between October and December.