The prime minister ordered an investigation into a possible breach of the ministerial code, saying there were “clearly” questions to be answered.
But Mr Zahawi will remain Conservative Party chairman during the inquiry.
The former chancellor dismissed reports of an HMRC review into his taxes – first revealed by The Independent last year – as a “smear”, but on Saturday he admitted he had settled a dispute and paid a penalty understood to be around £1m.
The new inquiry, by ethics adviser Sir Laurie Magnus, is also expected to look at threats Mr Zahawi made against those looking into his tax affairs – including to The Independent – and whether his initial denials were accurate.
However, Downing Street made clear the investigation would not reveal how much Mr Zahawi had to pay the taxman.
Labour Party chair Anneliese Dodds said: “The investigation into Nadhim Zahawi should be as wide-ranging as necessary, including his use of lawyers to shut down these questions.
“But Rishi Sunak shouldn’t need an investigation to know that Nadhim Zahawi isn’t fit for government. He needs to grow a backbone and sack him.”
Liberal Democrats deputy leader Daisy Cooper MP said: “These legal threats must be thoroughly investigated. The idea of a cabinet minister appearing to use legal threats to silence transparency campaigners is deeply troubling.”
Asked if Sir Laurie would be looking at Mr Zahawi’s threats, Mr Sunak’s spokesman said the investigation was “looking at potential breaches of the ministerial code relating to ministerial declarations in the first instance, but he [Sir Laurie] does have the ability to look at other issues if he thinks they are relevant”.
He said: “The prime minister thinks that it is right that the government acts with integrity and accountability. That is important to him.”
Downing Street also indicated that the prime minister did not know the former chancellor paid a penalty to settle the case, and that “additional facts” had been placed in the public domain by Mr Zahawi over the weekend.
“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,” the spokesman added.
Mr Sunak had told the House of Commons on Wednesday that Mr Zahawi “has already addressed this matter in full and there’s nothing more that I can add”. But pressed on whether Mr Sunak knew then that Mr Zahawi had paid a penalty to HMRC, the spokesman said: “That’s not my understanding.”
Labour leader Sir Keir Starmer said that Mr Sunak’s handling of the affair is “a test of the prime minister”.
The investigation will look at the code around ministerial declarations; under the guidelines, newly appointed ministers must set out all potential conflicts of interest.
The Independent first revealed last July that Mr Zahawi was being investigated by HMRC over the sale of shares in the polling company YouGov he co-founded in 2000.
At the weekend Mr Zahawi said he was judged to have made a “careless” error in the allocation of shares.
He also revealed that “questions were being raised” about his taxes when he was appointed chancellor by Boris Johnson in July and said the issue had been resolved before his next cabinet job – indicating that he was in charge of the Treasury, and ultimately, HMRC, when the dispute was settled.
He has not disclosed the size of the HMRC settlement – reportedly an estimated £4.8m, including a 30 per cent penalty of around £1m.
An ally of Mr Zahawi said on Monday that the former chancellor “absolutely” will not be quitting in the face of growing pressure over his settlement.
But senior Tory MPs have told The Independent the under-fire minister’s position as Tory chair is “untenable” and he is “unlikely” to survive.
The government would not be drawn on whether other government ministers are currently in dispute with HMRC, in response to a question in the Commons from Labour MP Cat Smith.
Cabinet Office minister Jeremy Quin replied: “This is a matter for individual ministers ... to go through the proper process for the ministerial code,” adding: “It is absolutely critical that no conflicts of interest are established or indeed perceived conflicts of interest are established.”
The renewed focus on Tory finances comes as Labour called on Mr Sunak to “abide by” his promise to release his tax return before the tax year lapses.
A No 10 source said: “The PM has committed to publishing his tax return and will do so in due course.”
And last night Labour also accused the government of failing to crack down on offshore tax avoidance, after parliamentary questions showed ministers have not assessed how much is in so-called ‘non-resident’ trusts, which can include those held by non-doms.
Rachel Reeves, Labour’s shadow chancellor said: “We knew that this Tory Government wasn’t working to tackle offshore tax avoidance. Now we know that they aren’t even monitoring the problem.”
The Treasury has been approached for comment.