The mining billionaire Gina Rinehart has demanded the National Gallery of Australia remove her portrait from an exhibition by the award-winning artist Vincent Namatjira.

The image, arguably an unflattering picture of Australia’s richest woman, is one of many portraits unveiled at the Canberra gallery as part of the Archibald prize-winning artist’s first major survey exhibition.

The National Gallery has rebuffed efforts to have the picture taken down and said in a statement that it welcomed public dialogue on its collection and displays.

“Since 1973, when the National Gallery acquired Jackson Pollock’s Blue Poles, there has been a dynamic discussion on the artistic merits of works in the national collection, and/or on display at the gallery,” it said.

“We present works of art to the Australian public to inspire people to explore, experience and learn about art.”

The portrait of Rinehart hangs alongside images of Queen Elizabeth II and football player Adam Goodes and is set to be on display until 21 July.

Before going on show in Canberra, the painting was on public display in Adelaide for months during the exhibition’s initial run at the Art Gallery of South Australia from October 2023 until January 2024.

The SA gallery has confirmed it did not field any requests for the removal of the painting.

A reproduction of the image is also part of a prestigious Thames & Hudson monograph about Namatjira’s work, published to accompany the survey show.

Rinehart is listed as a friend of the National Gallery after donating between $4,999 and $9,999 to the institution.

She has been contacted for comment through her company Hancock Prospecting.

In 2023, Rinehart withdrew a $15m sponsorship of Netball Australia after the Indigenous netballer Donnell Wallam asked for her uniform not to carry the Hancock Prospecting logo.

Rinehart later set up a $3m fund to reward athletes who won gold medals or set world records in swimming, artistic swimming, rowing and volleyball.

In 2020 Namatjira became the first Aboriginal artist to win the Archibald prize with his portrait of Goodes, with his paintings about changing people’s perspectives by using satirical humour as a commentary on power.

In one of his recent works included in the show, King Charles III stands in his regalia in the central desert, looking decidedly uncomfortable and out of place, as a way of depriving the royal family of their power and entitlement.

Born in Alice Springs, Namatjira was raised in foster care in Perth from the age of six, which meant losing his connection to family, country and culture.

He grew up not knowing of his link to the famed watercolourist Albert Namatjira – Vincent is his great-grandson – until he was an adult, and was astonished to discover his artistic legacy and the significance of his family name.