Under-fire Nadhim Zahawi has been urged to step down by his predecessor as Tory chairman.
Senior Tory Sir Jake Berry told the BBC it is "unsustainable" for the Mr Zahawi remain in the role while Rishi Sunak's ethics adviser investigates his tax affairs.
Piling pressure on the Tory chairman, Mr Berry said the Government "needs to find a mechanism for ministers and MPs who are under investigation to step aside" temporarily.
He said it is "unsustainable" for Mr Zahawi to remain in post.
It comes after the boss of HMRC suggested Mr Zahawi did not make an "innocent error" amid a toxic row over the Tory Chairman's tax affairs.
Rishi Sunak was this week branded "weak" by Labour for failing to remove the party chairman after it emerged he had paid a penalty to HMRC.
Mr Berry told BBC Question Time last night: “Even though he’s a friend of mine I’m not going to allow that to distract from a view I’ve put forward consistently in relation to all these sorts of issues.
“The Government needs to find a mechanism for ministers and MPs who are under investigation in this way to step aside to clear their name and then to come back into government if that is appropriate.
“I think from Nadhim, great individual that he is, that would be the right thing to do now.
“I applaud Rishi Sunak for fast forwarding this investigation that we learned this week will be concluded in around 10 days.
“But I do think it’s unsustainable for a minister to stay in his post while this investigation goes on, including other ministers who are also under investigation.
“Not least because we have learned that when you want the public to have faith and trust in these investigations, one of the key things is for that individual to step away from power because it takes away a perception they have some influence or an ability to alter the investigation because they remain in that position of power.”
Meanwhile the Institute for Government's Dr Hannah White told BBC Radio 4's Today programme: "If he had been suspended he wouldn't be trying to do his current job and facing embarrassing questions.".
Labour's Deputy Leader Angela Rayner told The Mirror: “Tory MPs know the game is up for Nadhim Zahawi and even the man he succeeded has called for him to stand aside, but Rishi Sunak still hasn’t read the writing on the wall.
"The Prime Minister has proven himself too weak to sack his Tory Party Chair and has once again shown his appalling judgement by continuing to prop him up.
"Instead of getting their house in order, they're all over the shop. It’s a total failure of leadership from this clapped-out Government. Britain deserves better."
Mr Zahawi has said a "careless but not deliberate" error had been made, relating to shares in YouGov, the polling company he co-founded.
In a statement at the weekend, he confirmed he had agreed to a settlement - estimated to be worth around £5million, including a penalty - while he was Chancellor in the dying days of Boris Johnson's Government.
Mr Zahawi has given HMRC approval to speak to the investigation into his tax affairs, a source close to the Tory chairman said.
Appearing in front of MPs on Thursday the permanent secretary at the tax office Jim Harra was asked what HMRC means when someone has been "careless".
He explained: "I'm not commenting on any particular person's affairs but carelessness is a concept in tax law.
"There are no penalties for innocent errors in your tax affairs.
"So if you take reasonable care but make a mistake whilst you will be liable for the tax and for interest if it's paid late you would not be liable for a penalty.
"If your error was as a result of carelessness, the legislation says a penalty could apply in those circumstances."
Mr Harra also told MPs on the Public Accounts Committee that if his officials at HMRC are asked they would assist the probe into Mr Zahawi.
"If we are asked by the independent adviser on ministerial interests to help with the inquiry, we will do so in any way we possibly can", the tax boss said.
Mr Harra also said that he could not comment on an individual's tax affairs, but signalled that HMRC could potentially offer a more public comment on a minister's tax affairs under certain circumstances.
