The party claimed reports at the weekend cast doubt on public statements from the government about when it was made aware of allegations against the former First Minister.
But the Scottish Government has hit back, saying the opposition were putting due process at risk by “playing politics”.
Mr Salmond is taking the Scottish Government to court to challenge its procedures for dealing with sexual harassment allegations against ministers, after two accusations were made dating back to his time in office.
Two allegations of sexual harassment were made in January against the former first minister, who strongly denies the claims. Mr Salmond, who has since resigned from the SNP, was informed of an investigation in March.
The Scottish Government stressed no complaints had been recorded prior to January after a report in the Daily Mail that one of those complaints was first investigated in 2013.
There were also reports in the Sunday Times that “several” new allegations have been passed to the SNP and were being examined by an independent lawyer. This could not be independently verified.
The SNP said “it would be inappropriate to comment on the existence or otherwise of complaints.”
Labour MSP Rhoda Grant said the latest developments were “extremely serious” and said her party would seek to bring a minister to Holyrood for a statement.
“It is absolutely essential that the complaints procedure – and the timeline to this point, including who knew what and when – are clear and transparent,” Ms Grant said.
“The SNP government is in danger of throwing up a smokescreen around this situation and eroding public trust in this process.”
A spokeswoman for the First Minister said the two complains received in January “are the only recorded complaints that the Scottish Government has received about Mr Salmond”.
“Of course, as soon as it is able to the Scottish Government will make available as much information as it can, whilst respecting the privacy of those involved.
“And at that time the First Minister will be more than willing to address these issues in Parliament. However for legal reasons it is not possible to do so at present.
“To seek to play politics on issues that demand proper due process risks doing a disservice to those who have raised complaints.”
A spokesman for Mr Salmond said: “A Petition for Judicial Review will very shortly be called in the Court of Session where we intend to demonstrate that the complaints procedure deployed against Alex by the Scottish Government was unlawful.
“We will do our talking in that court.”