Coalition Senator Jacinta Nampijinpa Price has said her wearing of a Donald Trump-style hat was a "joke".

Speaking at the Royal Darwin Hospital Thursday, where the Opposition announced they would match Labor's $60 million commitment to aged care in the top end, Senator Price also attacked the media for their coverage of politicians' social media.

On Sunday, images of the NT Senator wearing a "Make America Great Again" hat—made famous by US President Donald Trump—alongside her partner Colin Lillie at Christmas last year came to the fore, less than a day after the Opposition spokesperson for Indigenous policy said her vow to make Australia great again was not an ode to President Trump.

After not commenting on the subject for days, Senator Price told reporters the hat was a Christmas gift, which was "a stunt" and a "joke in her family".

"If the media want to sensationalise four words that belong to the English language — and why shouldn't any of us be able to use those words — that's ridiculous," she said.

Her comments on Saturday and later revealed image were seized on by those in Labor, with sources on the East Coast calling it too good to be true, whilst Health Minister Mark Butler said the Coalition had said the "quiet part out loud".

"Australia is the best country in the world. And if Jacinta Price doesn't realise that, that's really disappointing. What she said today tells us that they just want to import US policies and US slogans to Australia. The only thing she didn't have today was the hat," he said on Saturday.

The Celtic/Warlpiri woman, who was criticised by Noongar protestors at event in Bunbury last week, said journalists should realise family issues and personal social media pages are out of bounds.

"Everything that I have is on private, so someone's dug in there and I think that's really quite low," Senator Price said.

"I don't have to explain myself to the Australian people for wearing a Christmas gift and taking a photo of myself."

In an op-ed in The Australian on Thursday, she went further, arguing her comment to "Make Australia Great Again" was because she "wanted to see Australia returned to its former glory".

"And what I meant by that was exactly what I said. That I want the damage to be reversed; that I want our country's trajectory to begin to point true north again; that we might begin to see some semblance of restoration, redemption – dare I say it, greatness," she said.

The NT Senator said the media's "dumbing down" had let Labor off the hook over national security, while an "absence of adult conversations" had occurred after she used the slogan on Saturday, saying "those comments didn't make the headlines because they didn't fit the separatist narrative".

"But again, these things require more than a headline to understand, so for many people it goes unnoticed," Senator Price wrote.

"I believe the media's dumbing down bears a significant responsibility for that. As an aside, the media also bears the burden of having made gifts I got at Christmas somehow more important than the cost-of-living crisis."

@natindigtimes In her opening remarks at a recent Liberal Party event in Bunbury, Senator Price told the attendees "marginalised Indigenous Australians" need "less government" involvement. #indigenousaustralia #aboriginalaustralia #jacintaprice #liberalparty #auspol #politicalprotest #indigenoustiktok #bunbury ♬ original sound - National Indigenous Times

In response to questions about saying "Make Australia Great Again" on Saturday, she told reporters in Boorloo/Perth she didn't "even realise I said that" before arguing it was not "an ode" to the president.

"Let's be very, very clear, media, you're obsessed with Donald Trump. We're not obsessed with Donald Trump. We're actually obsessed with ensuring that we can improve the circumstances for Australians," Senator Price said.

In January, Senator Price was appointed shadow minister for government efficiency to help clean up "wasteful spending", in what at the time seemed like a nod to the Elon Musk-led Department of Government Efficiency under the Trump Presidency - despite another Coalition MP already holding a similar shadow portfolio.

Since then, polling numbers have declined for the Coalition, with a key focus of Labor's campaign to focus on Mr Dutton's perceived extremism and the suggestion he is Australia's counterpart to President Trump.