The Albanese government has sharpened its attacks on One Nation as a party of “stunts and the vibe” after the South Australian premier warned Pauline Hanson is a threat to Labor following its historic state election result.

The federal Coalition is also dialling up the pressure, warning One Nation to expect more scrutiny of its policy positions as it attempts to avert a SA-style collapse in other parts of the country.

One Nation could have up to seven MPs across both houses of the SA parliament after Saturday’s ballot, where it outpolled the Liberal opposition with more than 22% of the primary vote.

While its vote was strongest in once-safe Liberal seats in regional and rural areas, the right-wing populist party also polled more than 30% in several outer suburban Labor electorates.

Labor is expected to retain all of those seats due to preference flows but the swings to One Nation demonstrate the risk it poses to both of the major parties.

Asked on Monday if One Nation was a threat at the federal level, the South Australian Labor premier, Peter Malinauskas, said: “Yes, I do”.

“I think we have got to treat this seriously. I don’t think One Nation or any political party for that matter should be written off,” Malinauskas told Nine’s Today show.

“I think it is worthy of not demeaning anybody or diminishing anyone else’s point of view but understanding what informed that surge. And I think there are implications for my party as much as there are for the Liberal Party.”

Laying out a potential template for his federal counterparts, the SA premier has put forward an alternative, progressive case for patriotism to counter Hanson’s version of national pride.

One Nation’s sole lower house MP in Canberra, Barnaby Joyce, said Labor was targeting the party because it was viewed as the “authentic opposition”.

“They have to play the man because they quite clearly know that One Nation clearly stands for something and clearly is the alternative to Labor,” he told Seven’s Sunrise.

The deputy prime minister, Richard Marles, used question time to attack One Nation as a party that has “only ever been about stunts and the vibe”.

The Labor Party federal president, Wayne Swan, went further, claiming One Nation was offering “no alternative economic agenda, just culture-war camouflage for a wealth concentration agenda”.

“Barnaby Joyce’s hollow triumphalism is revealing. He’s cheering on a movement that flew to Mar-a-Lago with billionaires to learn how to run elections but hasn’t spent a minute developing serious policies to address Australians’ real challenges,” Swan told Guardian Australia.

“This is politics imported wholesale from the American and British hard right. These are the same forces that delivered thirty years of wage stagnation in the United States, hollowed out the middle class, and gave the world Donald Trump and Brexit.”

The collapse of the Liberal vote in SA has prompted a fresh round of soul-searching inside the federal Coalition, where MPs hold competing views about how best to respond to One Nation’s rise.

The Angus Taylor-led opposition is widely expected to announce a new plan to lower immigration ahead of the 9 May Farrer by-election – the first federal test of Hanson’s support.

Other MPs are pushing to instead prioritise economic policies, including tax reform, to help rebuild the party’s economic credentials.

SA Liberal senator and the party’s state president, Leah Blyth, said voters were making a “deliberate choice” to abandon it for One Nation.

“The One Nation vote is not the problem, it is the symptom. It reflects voters who no longer feel we are speaking clearly or standing firmly,” she said.

“If we are serious about governing again, we need to be serious about who we are not who we think we should sound like.”

The shadow immigration minister, Jonno Duniam, signalled One Nation would face more scrutiny of its policies in the wake of its success in SA.

“If they are serious about being a major party, which is what their leader senator Hanson says, then they can be held to the same standard as Angus Taylor and Anthony Albanese are around details because I think that’s what’s going to make a difference,” he told Sky News.