Ian Blackford said there is “tremendous sadness” that Mr Salmond, who led the SNP for 20 years, has now quit the party - but also stressed that the interests of the two complainers who had come forward are paramount.
He was speaking after former first minister Mr Salmond’s crowdfunding appeal smashed through its £50,000 target within hours of being launched.
By 4pm on Thursday, he had raised more than £80,000 towards his legal action at the Court of Session in Edinburgh.
But his fundraising bid was blasted as “astonishing” and “unbelievable” by opposition politicians.
Meanwhile Ms Sturgeon, who succeeded Mr Salmond as First Minister in 2014, appealed on social media to her followers to donate to a campaign to fund a legal challenge to the UK Government’s so-called “rape clause”.
Mr Salmond announced on Wednesday night that he had given up his membership of the SNP, 45 years after he first joined the party.
The shock move came after Ms Sturgeon had faced calls to suspend him from the party after allegations of sexual misconduct, dating back to Mr Salmond’s time as first minister, had emerged.
The former leader said he had given up his membership in a bid to prevent internal division within the SNP.
Mr Salmond, who strongly denies the claims against him, also stressed his “absolute intention” to rejoin the SNP “just as soon as I have had the opportunity to clear my name”.
Mr Blackford, speaking to members of the Scottish Parliamentary Journalists’ Association, dismissed any suggestion the former leader’s resignation could split the party, insisting it is “pretty united”.
Asked about Mr Salmond’s resignation, he said: “My overriding emotion is one of great sadness.”
But he added: “I think what has to be paramount in this are the interests of those who have come forward. We need to make sure that people can come forward, fulsome in the knowledge that they will have anonymity, that they will be listened to, and that action that needs to be taken will be taken.
“That’s the single most important factor out of all of this.”
Mr Blackford also said: “It’s up to individuals on a private basis what actions they’ve taken in relation to the crowdfunding.
“I’m not going to get into what individuals do, but I think you can interpret my remarks that I give absolute full support to the Government... and I am absolutely fulsome in my support for the First Minister.
“This is a party, a movement, that is pretty united.
“I am not getting messages from people suggesting that there is civil war within the SNP, far from it.
“What we have said is that we cannot treat anybody, whoever they are, any differently from how we would treat an ordinary party member.
“I think there is a maturity in general within the SNP. There is strong support for the First Minister, for the Government.”
The two complaints against Mr Salmond were raised in January and he was informed of an investigation by the Scottish Government in March.
Police Scotland confirmed on Friday that the complaints have been passed to the force.
Mr Salmond is now taking court action against the Scottish Government, with papers lodged at the Court of Session in Edinburgh on Tuesday.
He reiterated his strong denial of the allegations as he announced his resignation, saying: “Let me be clear again. I refute these two complaints of harassment and I absolutely reject any suggestion of criminality.”
A spokesman for the Scottish Conservatives said: “Scotland now faces the incredible and unprecedented situation of its most famous former first minister appealing to SNP supporters for cash to take legal action against the Government he used to run.”