Prime Minister Malcolm Turnbull will leave the “commentary to the commentators” when it comes to the fracas within One Nation.

In South Australia on Saturday where he joined Liberal candidate Georgina Downer for the July 28 Mayo byelection, Mr Turnbull refused to weigh in on whether the coalition would snap up ousted One Nation senator Brian Burston as they had former Jacquie Lambie Network senator Steve Martin.

“We work hard under the leadership of Mathias Cormann in the Senate to persuade everybody, regardless of which party they are in, to support our measures,” Mr Turnbull said.

One Nation’s Brian Burston is refusing to quit his Senate seat, undercutting Pauline Hanson’s power base unless she can force him out.

Senator Hanson sent her long-time supporter a letter on Friday demanding he resign from the Senate to allow her to pick a replacement.

“I no longer have confidence in in you as an officer of Pauline Hanson’s One Nation party,” Senator Hanson’s letter said.

Mr Turnbull, clad in his leather jacket and mindful of the approaching byelection, announced $10 million in funding for Adelaide’s Mount Barker Mountain Pool.

“Why can we deliver the funding for this pool?” Mr Turnbull asked.

“We can deliver it because we have brought the budget back under control.”

Ms Downer, the daughter of a former Howard government minister, has worked as a lawyer, diplomat and research fellow at a conservative think-tank.

“She is a local. She learnt to swim in this pool. Her roots are in this electorate, in this community,” Mr Turnbull said.

“Georgina is presenting herself as an advocate, as a powerful advocate but one who can work within the government.”

Burston says he won’t resign

Meanwhile, Senator Burston is refusing to go, which means Senator Hanson’s crucial three-vote bloc in the upper house is cut to two, vastly undercutting her influence.

“I will not be resigning from One Nation and I most certainly will not ever be resigning from my senate position,” Senator Burston told 2GB radio on Friday.

Liberal Democrat senator David Leyonhjelm confirmed he had talked to Senator Burston after Friday’s fracas.

“He’s determined not to resign… But he will be voting independently from One Nation,” Senator Leyonhjelm told AAP.

The crisis started when Senator Burston publicly revealed his plans to vote for the government’s company tax cuts, after Senator Hanson reneged on a deal to back them.

An intermediary also spent two weeks trying to set up a meeting with the Shooters, Fishers and Farmers party in NSW so Senator Burston could defect.

The party didn’t want him – but Senator Burston claims he wasn’t aware of the approach.

Queensland Liberal senator Amanda Stoker said it was to Senator Burston’s credit that he wasn’t “flip-flopping according to the whims and needs” of One Nation’s electoral prospects.

But Senator Hanson needed to re-evaluate her management style.

“There comes a point where you say, ‘after 20 or so people have come and gone from my partyroom, maybe it’s me’,” Senator Stoker told the ABC.

Twenty one people have either quit parliament, the party, been disqualified or expelled from One Nation while in parliament.

-with AAP