Many SNP members feel “dismayed and quite shocked” by recent events, MSP Michelle Thomson has said.
Ms Thomson, who ran Kate Forbes’ leadership campaign, said Humza Yousaf deserved the full support of the party.
There is an ongoing police investigation into the party’s finances which saw its former chief executive, Peter Murrell, arrested last week and later released without charge as enquiries continue.
SNP president Mike Russell has described the current period as the party’s biggest crisis in 50 years.
Ms Thomson, the MSP for Falkirk East, said there needed to be improvements in the governance of the party.
“So frankly, he now needs support to get on with a very, very challenging job right now.”
She continued: “There’s issues around the lack of governance, and I think many people in the SNP, many members, feel dismayed and quite shocked at events.”
Ms Thomson said the SNP’s rules around the membership of those who had been charged with crimes were unclear.
The MSP said: “He (Peter Murrell) is innocent until proven guilty. He has not been charged with a crime.
“That may change, but we need to be clear about what specifically are the rules.
“I’m certainly not clear about that and I’ll be asking about what the position is.”
In 2015 party bosses suspended Ms Thomson – who at that point was an MP – while police investigated property deals.
She denied any wrongdoing and criminal proceedings were never brought. In 2019 she rejoined the SNP.