Keith Brown said his party hoped to set a standard for transparency in Scottish politics.
The SNP has been described as the “most transparent party” by its depute leader despite a police probe into finances.
Keith Brown acknowledged the “internal challenges” facing the SNP but said First Minister Humza Yousaf was addressing outstanding transparency concerns.
A transparency row erupted within the party after former chief executive Peter Murrell resigned after denying the party had dropped around 30,000 members, a claim which the SNP then confirmed was accurate.
Police are investigating how more than £600,000 of donations earmarked for independence campaigning were spent, with Mr Murrell and former treasurer Colin Beattie arrested and then released without charge pending further investigation.
Speaking on BBC Scotland’s the Sunday Show, Mr Brown said: “In the meantime, we are one of the most transparent parties in the UK, you will have a very good idea of the SNP membership … do you know what the membership numbers are for the Scottish Tories or the Labour Party in Scotland?”
When challenged on the remark, he added: “You can’t just gloss over the fact they haven’t misled us (on party numbers), they haven’t told you.
“We are the most transparent, most successful party … in Scotland.
“We have to increase that transparency. It is my ambition – and I know that it’s Humza’s – to make sure that we are the most transparent party in Scotland and that we set the standard for transparency and shame other parties.”
Scottish Tory chairman Craig Hoy appeared on the programme after Mr Brown as he called the remarks “bizarre” and claimed the SNP was “addicted to secrecy”.
In an earlier interview with Sky News, Mr Brown also said he had not been notified until recently that party auditors Johnston and Carmichael resigned.
The First Minister only learned of the revelation after he replaced Nicola Sturgeon in the top job – despite the auditors stepping aside in around October.
Mr Brown said he only became aware “shortly” after the news became public. However, he said it was standard practice that Mr Yousaf would not have known prior to taking the role as he was not on the party’s national executive committee where these issues were discussed.
The SNP are searching for new accountants in time for the submission of audits to the Electoral Commission in July.
