Two people have made complaints against former first minister Alex Salmond, who denies ever sexually harassing anyone.
His successor, Nicola Sturgeon, said the complaints were made in January and were investigated through a process she had agreed to.
She said the situation was "difficult for me to come to terms with" given her long history with Mr Salmond, but claims "could not be ignored".
Mr Salmond told BBC Scotland he was "no saint" and has "got flaws".
He added: "I have made many mistakes in my life, political and personal.
"But I have not sexually harassed anyone and I certainly have not been engaged in criminality."
He also insisted that a new complaints procedure introduced by the Scottish government last year following wider concerns about harassment at Holyrood and Westminster was "unfair and unjust".
Police Scotland has confirmed that it is "carrying out an assessment of information which we have received and inquiries are at an early stage".
The Daily Record, which broke the story on Thursday night, says the allegations date back to December 2013, and that Mr Salmond has been reported to police over claims he sexually assaulted two staff members at the first minister's official residence at Bute House in Edinburgh.
In a BBC Scotland interview, Ms Sturgeon did not give any further details of the allegations or the outcome of the government investigation.
She also said she was "acutely aware how upsetting this will be" for her party, but stressed that "complaints could not be ignored or swept under the carpet".
Ms Sturgeon revealed that she first heard about the investigation from Mr Salmond in April and had no prior knowledge of complaints being made against him.
Asked if Mr Salmond was still a member of the SNP, the first minister said: "These matters will be considered in the fullness of time".
Mr Salmond has dropped legal action aimed at preventing the Scottish government revealing details of its investigation, but has asked the Court of Session in Edinburgh to review the government's handling of the complaints process.
He argues that new procedures introduced last year following wider concerns about sexual harassment at Holyrood and Westminster were "unfair and unjust".
The Scottish government claimed a statement released by Mr Salmond contained "significant errors", with Ms Sturgeon saying it would "defend its position vigorously".
Mr Salmond, who had two spells as leader of the pro-independence SNP, led the devolved Scottish government as first minister from 2007.
He quit in the aftermath of the independence referendum in 2014, when Scotland voted to remain in the United Kingdom.
Analysis by BBC Scotland political editor Brian Taylor
This is the last thing that the SNP wanted.
Nicola Sturgeon's gloomy demeanour during the interview rather said it all.
It affects her directly in three ways.
First of all it affects her governmentally because she is the political head of the government and she instigated this very policy of zero tolerance of sexual misconduct.
Secondly, it affects her politically because she is the leader of the SNP and depending on how it develops, depending on the outcome, this is scarcely potentially good news for the party.
And thirdly, it affects the first minister personally. She is a personal friend of Alex Salmond. He was her mentor, he was her predecessor as first minister.
Ms Sturgeon confirmed: "Complaints were made in January relating to Alex Salmond by two individuals.
"These complaints have been considered since then under a procedure covering ministers and former ministers that was agreed by me in December 2017 in the wake of public concern about harassment.
"Although I have been aware for some time of the fact of the investigation - initially from Alex Salmond - I have had no role in the process, and to have referred to it before now would have compromised the integrity of the internal investigation, which I was not prepared to do."
Ms Sturgeon said she had been told by the Scottish government's top civil servant, Leslie Evans, earlier this week that she had completed her investigation and that she intended to make the complaints public.
The first minister added: "Alex Salmond is now challenging the Scottish government's procedure in court. The Scottish government refutes his criticisms of its process and will defend its position vigorously.
"I have been clear on many occasions that all organisations and workplaces must make it possible for people to come forward to report concerns and have confidence that they will be treated seriously.
"For that principle to mean anything it cannot be applied selectively. It must be applied without fear or favour, regardless of the identity, seniority or political allegiance of the person involved."
- Leader of Scottish National Party 1990-2000 and 2004-2014
- First Minister of Scotland 2007 - 2014
- Stood down after Scotland voted to remain in the United Kingdom
In a statement released on Thursday night, Mr Salmond strongly denied all of the allegations against him. He did not say what the claims were, but described some of them as being "patently ridiculous".
He also said that "on the advice of Senior Counsel" he had been complaining to Mrs Evans, the Scottish government's permanent secretary, that the complaints procedure was "unjust" and "unlawful".
The permanent secretary is responsible for the Scottish government's 5,000 civil servants, and is the principal policy advisor to Ms Sturgeon.
Mr Salmond said that "with great reluctance" he had now launched a judicial review against the Scottish government at the Court of Session.
He said that if he lost the case he would have to answer to the complaints against him "both comprehensively and publicly".
But he warned that "the administration at the senior levels of the Scottish government will have the most serious questions to answer" if the court finds in his favour.
Mr Salmond said: "Even now I have not been allowed to see and therefore to properly challenge the case against me.
"I have not been allowed to see the evidence. I have tried everything, including offers of conciliation, mediation and legal arbitration to resolve these matters both properly and amicably.
"This would have been in everybody's interests, particularly those of the two complainants. All of these efforts have been rejected."
Mr Salmond was elected as the SNP MP for Gordon in 2015 before losing the seat in the snap general election two years later.
He has faced heavy criticism for hosting the Alex Salmond Show on Russian broadcaster RT, which has been described as a propaganda channel for the Kremlin - a claim Mr Salmond has denied.
RT has said that the show would continue to be broadcast "at this time".