Humza Yousaf has admitted the governance of the SNP “was not as it should be”.
Scotland’s new first minister also said with the removal of power couple Nicola Sturgeon and Peter Murrell from the top of the party, it would allow an opportunity to “have a different way of doing things”.
Mr Yousaf said it had been a “difficult 24 hours” following former SNP chief executive Mr Murrell’s arrest amid a police probe into party funding and finances.
Ms Sturgeon’s husband and the former SNP chief executive was taken into custody to be questioned by detectives on Wednesday before later being released without charge.
Speaking to media at Bute House in Edinburgh on Thursday, Mr Yousaf said: “Whatever else transpires in this case, it is very, very clear that the governance of the party was not as it should be.
“It was not at its best standard. And frankly, the debacle over membership numbers is just one example of that.”
Mr Yousaf said he has not yet spoken to his predecessor.
He told Sky News: “I’m sure we’ll see each other when parliament reconvenes after the Easter recess, but we’ll certainly not be discussing a live police investigation.
“That would be inappropriate to do for all manner of means.”
Ms Sturgeon announced her shock resignation in February after more than eight years as first minister.
Mr Yousaf was formally sworn in as Scotland’s new leader last week.
Mr Murrell, who married Ms Sturgeon in 2010, resigned as SNP chief executive last month after more than 20 years in the role.
He was forced to step down after shouldering the blame for the party’s misleading responses to the media over membership numbers.
Speaking about Ms Sturgeon, Mr Yousaf said: “I think in her own view and her own words, she was a dominant political force.
“There’s now an opportunity with her no longer the leader of the party, with Peter no longer the chief executive, to have a different way of doing things.”
The long-running police probe is linked to the spending of around £600,000 raised by supporters to be earmarked for Scottish independence campaigning.
Mr Murrell and Ms Sturgeon’s home in Glasgow was taped off and a police tent erected outside.
Officers were also seen removing boxes from SNP headquarters in Edinburgh.
Mr Yousaf said: “There’s no getting away from the fact that it’s a difficult 24 hours. And it comes after quite a challenging election contest, as election contests tend to be.
“But we’ve got a new leader, there will be a new chief executive of the party.
“Our party is not built on one person, or indeed even one or two people. We are a strong party. We’ve got a strong message, a good track record of delivery as a government.
“And that’s why I want to get back to talking about the priorities of the Scottish people, but there’s no doubt, of course the last 24 hours have been challenging.”
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In the earlier press conference, the first minister said he had not been in contact with the police himself but the SNP had been cooperating with the investigation.
He said one of the first conversations he was “keen to have” as the new leader was to “understand the party’s finances” and get “up to speed” on the police probe.
Mr Yousaf said: “I wanted to in my very first NEC meeting make sure that the NEC agreed to a full review in terms of governance and transparency with external input.
“I think that last part is important because there are members and the public and our press rightly have questions that they want answered around these issues.
“And frankly, a review of governance, a review of how we do things as transparently as possible is clearly needed.”
Mr Yousaf said he would “have to check” if Mr Murrell was still an SNP member but added that Ms Sturgeon would not be getting the whip removed.
He said: “Remember, our justice system works on the premise, quite rightly, that people are innocent until proven guilty.”
Speaking to Sky News’ Beth Rigby last month, Ms Sturgeon would not comment on the police investigation but said it played no part in her decision to step down.