Rishi Sunak has ordered an investigation into Nadhim Zahawi as he resisted calls to sack the Tory party chairman over his multimillion-pound tax dispute.

The prime minister asked new ethics adviser Sir Laurie Magnus on Monday to assess whether the cabinet minister breached the ministerial code with the HMRC settlement he made while he was chancellor, but it could extend to his prior tax arrangement and whether he lied to the media.

Mr Sunak retained confidence in the former chancellor but said he was launching an investigation because “clearly in this case there are questions that need answering”.

He added that he was not leader at the time of the allegations and insisted the advice he received when he gave Mr Zahawi a senior role was there was “no reason” not to appoint him.

But Labour leader Sir Keir Starmer said: “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.”

Politics live: Zahawi told to quit – amid ‘clear evidence’ TV interview defence was ‘not true’

Scotland’s first minister, Nicola Sturgeon, has also said Mr Zahawi’s position is “untenable”.

Earlier, a source close to the embattled Tory MP said he is “absolutely not going to resign” in the face of growing pressure over his settlement, estimated to be around £5m.

The government’s paymaster general, Jeremy Quin, told the Commons on Monday the process for the management of conflicts of interest, or potential conflicts, is “clear and robust”, however the PM has the ultimate say on appointments.

But he added: “It is a responsibility of all ministers to ensure that no conflict arises or could be reasonably perceived to arise between their role and their interests, financial or otherwise.”

The tax expert who investigated Mr Zahawi has joined calls for him to go, telling Sky News there is “clear evidence” he has not been truthful about his affairs.

Dan Neidle, the Founder of Tax Policy Associates and a Labour member, pointed to comments made by Mr Zahawi to Kay Burley last summer, while the then-chancellor was running to be leader of his party.

Mr Zahawi said he was “clearly being smeared” over questions about his affairs – and that he did not “benefit” from an “offshore trust”.

Speaking to Kay Burley on Monday, Mr Neidle said that a filing disclosure from YouGov – the polling company Mr Zahawi co-founded – showed he “received £99,000 from Balshore Investments”, a company based in Gibraltar.

Mr Neidle said: “That’s not my supposition or a guess – it’s absolute fact.

“And yet he denied that to you.”

Mr Neidle said there could be “an innocent explanation” for Mr Zahawi’s tax error, which the Tory MP called “careless not deliberate”.

But he added: “I lack the imagination to see it and if there isn’t one, I think he should resign.”

What we still don’t know about Zahawi’s tax dispute

Questions about Mr Zahawi’s tax affairs have continued, even after he released a statement to “address some of the confusion about my finances”.

On Saturday he admitted he paid what HMRC said “was due” after it “disagreed about the exact allocation” of shares in YouGov.

But he did not disclose the size of the settlement – reported to be an estimated £4.8m including a 30% penalty – or whether he paid a fine.

Sky News understands he did pay a fine, and Mr Neidle said the use of the word “careless” confirms this.

He said “careless means something specific” in tax terms – “that you didn’t behave in a reasonable way”.

“A reasonable way is you instruct decent tax advisers. You tell them the truth, you follow their advice, you check your final tax returns as best you can.”

It is also not clear how much money Mr Zahawi made before settling the dispute.

Mr Neidle said: “I think he would have received about £27m and not paid tax on it until eventually he was forced to because it was being reported. He didn’t admit it, denied it, threatened to sue people and went to HMRC to quietly settle it.”

Mr Zahawi did not answer questions from reporters as he headed into the Conservative Party headquarters in Westminster earlier on Monday.