Rishi Sunak has ordered an investigation into Nadhim Zahawi as the Tory party chairman faced growing calls to quit after paying a penalty to resolve a multimillion-pound tax dispute.

Nicola Sturgeon has called on Mr Zahawi to resign, insisting his position as chairman of the Conservative party is "untenable".

The Prime Minister has asked his new ethics adviser Sir Laurie Magnus to assess whether the former chancellor breached the ministerial code with the HMRC settlement.

Mr Sunak said the minister, who is defying Labour demands for his resignation, would stay on during the inquiry, launched as a series of scandals mounted.

Read more: Nicola Sturgeon agrees to publish seven years of tax returns

Mr Sunak told broadcasters: “Integrity and accountability is really important to me and clearly in this case there are questions that need answering.

“That’s why I’ve asked our independent adviser to get to the bottom of everything, to investigate the matter fully and establish all the facts and provide advice to me on Nadhim Zahawi’s compliance with the ministerial code.

“I’m pleased that Nadhim Zahawi has agreed with that approach and has agreed to fully co-operate with that investigation.”

Read more: Tory minister says tax affairs of cabinet are 'private matters'

In a statement, Mr Zahawi said: “I welcome the Prime Minister’s referral of this matter to the independent adviser on ministerial standards.

"I look forward to explaining the facts of this issue to Sir Laurie Magnus and his team.

“I am confident I acted properly throughout and look forward to answering any and all specific questions in a formal setting to Sir Laurie.

“In order to ensure the independence of this process, you will understand that it would be inappropriate to discuss this issue any further, as I continue my duties as chairman of the Conservative and Unionist Party.”

Speaking to journalists the First Minister said Mr Zahawi should step down from his role.

Ms Sturgeon added: “I think his position … is untenable. I think he should resign his current position as chair of the Conservative Party.

“It seems to be the case … that while he was Chancellor he settled a seven-figure tax bill with HMRC which included a very significant penalty.

“That means, as far as I can see, that there must have been something untoward about his tax affairs to a very large tune, in terms of the amount of money involved.

“I think somebody who is a Government minister in that position, I just think their position is untenable.

“I would think he should resign his post, and if he doesn’t do so, rather than kicking it into the long grass and instructing an inquiry – as the Prime Minister has done this morning – I think the Prime Minister should remove him from office.”

Read more: Kemi Badenoch snubs Holyrood committee over gender reforms block

Labour leader Sir Keir Starmer has also said Mr Zahawi’s position was “untenable” and he should be sacked.

He told reporters: “I think it’s obvious that Zahawi can’t stay as Tory Party chair, the very idea that he can be discussing and negotiating his own tax affairs with the body that he’s supposed to be running, everybody knows it’s wrong.

“He clearly isn’t going to resign and so the Prime Minister needs to show some leadership.

“This is a test of the Prime Minister. He promised us – his first words – integrity and accountability.

“Well, if those words mean anything, the Prime Minister should sack him, and sack him today and show some leadership.

“Because if he doesn’t, it’s just going to be further evidence, I think, for the British public, as to just how weak this Prime Minister really is.”

Failing to sack Mr Zahawi would be a “strong failure of leadership” and “if this was somebody in my team, I would sack them”, Sir Keir added.

Downing Street suggested the Prime Minister was not aware last week that Mr Zahawi had paid a penalty to settle his tax dispute with HMRC.

The Prime Minister’s official spokesman said: “Subsequently, over the weekend additional facts have been placed in the public domain by the chairman.

“As you heard from the Prime Minister this morning, he thinks it’s right because of this to ask his independent adviser to establish the facts.”

Number 10 also said that the investigation will focus on ministerial declarations but could extend to whether his tax arrangements were appropriate.

The Prime Minister’s official spokesman said: “He is focused on potential breaches of the ministerial code relating to ministerial declarations. But it will be up to him if he wishes to look into any other issues as well.”

Asked if this could include whether Mr Zahawi lied to the media, the official said: “The adviser is able to look more widely if they see fit.”

Asked whether Sir Laurie could look at whether Mr Zahawi’s tax arrangement was a suitable one for a minister, the spokesman said: “His role is to establish potential breaches of the ministerial code, so that potentially could fall within that remit, but I wouldn’t seek to be too prescriptive.”