First Minister Nicola Sturgeon said there was "no legal basis" to suspend Alex Salmond for alleged sexual harassment from the SNP.
She said her party had received no complaints about the behavior of her predecessor – and would not have conducted the investigation – but the matter would be reconsidered when the situation changes.
It comes after the opposition parties have asked SNP to suspend Mr Salmond for what he denies.
Ms Sturgeon said: "As SNP leader, it is important for me to present the reasons for the current position of the party as clearly as possible.
"The SNP, like all organizations, must act in a proper manner.
"In this case, unlike some previous cases, SNP did not investigate complaints about Alex Salmond and the party has received no complaints."
She added, "Also for legal reasons, the limited information that I have on the investigation of the Scottish Government can not be shared with the party at this time – and rightly it is the party, not me, as a leader, that membership can suspend.
"In summary, the party has no legal basis at this time to suspend Alex Salmond's membership.
"If this situation changes, of course, the matter will be rethought as for each member.
"The rules of the party apply to all members and nobody stands above them."
Allegations of the conduct of Mr. Salmond against two employees in 2013 – during his tenure – were transferred to Police Scotland.
Leslie Evans, Secretary of State for the Scottish Government, said the complaints had been filed in January and Mr Salmond was informed of an investigation in March.
She intends to make a statement on the complaints, but the move was halted after the former first minister initiated a lawsuit.
Scottish Labor has now demanded transparency from the Scottish Government for meetings between First Minister Nicola Sturgeon and her predecessor Alex Salmond during an investigation into allegations of sexual assault against Mr Salmond.
It is clear that Alex Salmond and Nicola Sturgeon have met several times to discuss the case.
Labor has said the government should publish the dates, dates and details of these meetings and clarify whether Mr. Salmond has ever asked the first minister to interfere in any way with the investigation.
Scottish Labor Manager and Women's Spokesperson, Rhoda Grant MSP, said last night: "The Scottish people expect full transparency in this case.
"It is clear that Alex Salmond has met the first minister several times to discuss the investigation of allegations of sexual assault.
"It would be totally unacceptable if the details of these meetings were not known.
"The allegations against Alex Salmond are incredibly serious, and his meetings with the head of a government investigating him must not be kept under wraps.
"Nicola Sturgeon must publish the details and minutes of these meetings as soon as possible.
"The SNP must do everything in its power to give the complainants the support they need, whoever the alleged perpetrator is, and make it clear that there is a safe room for all other survivors.
"In the meantime, Nicola Sturgeon should immediately suspend Alex Salmond from the SNP."
Gordon MP Colin Clark, who had toppled Mr Salmond yesterday in last year's elections, would not be included in the debate over whether or not his voter should step down from the SNP.
Mr. Clark said, "The accusations are very serious and the complaint process must be followed, and everyone should be considered innocent until proven guilty and no one, not even the first minister, is above the law."