It is claimed corruption complaints and criticisms of senior officers were removed from an internal report into the early days of the amalgamated police force.
The Conservatives, Labour and the Liberal Democrats all said the claims, which are made in a new TV documentary about the national force, raised serious questions for the Scottish Government.
Tory justice spokesman Liam Kerr has tabled an urgent question at Holyrood and said: “The allegations would suggest that some Scottish police officers have, at the very least, been conducting themselves in a highly questionable manner.”
Meanwhile both Labour and the Liberal Democrats want Mr Matheson to make a statement to MSPs on the issue.
It comes after a BBC Scotland investigation raised concerns that bad practices and unlawful behaviour in the previous eight regional forces had continued after Police Scotland was established in 2013.
A report was commissioned by former chief constable Sir Stephen House in 2014, a year after the single national force began.
A BBC Scotland investigation claims drafts of the report show the chief constable’s office wanted negative comments deleted, tenses changed to suggest problems had been fixed, and an entire section, where frontline officers described working in a culture of fear, removed.
The investigation also claimed early drafts of the report detailed officers conducting unauthorised surveillance, threatening and intimidating witnesses, unlawfully detaining suspects, colluding while compiling statements and failing to reveal evidence, but these were removed from the final version.
Police Scotland said “significant changes” have been implemented in the four years since the report and Iain Livingstone, the current interim Chief Constable, has “already acknowledged that in the early days of Police Scotland process was put ahead of people”.
The Met Police, where Sir Stephen is now an assistant commissioner, said he was not commenting on the report.
Mr Kerr however said: “The allegations in this investigation are extremely serious and shocking.
“If true, this is evidence that the Chief Constable of Police Scotland intentionally misled the Scottish Government and the general public about working practices at Police Scotland.”
He added: “I have tabled an urgent question demanding a full and detailed response from the Justice Secretary and the Scottish Government.
“It is vital that we know exactly what role the SNP has been playing, what they knew and when.
“This is yet another allegation of serious misconduct at Police Scotland. At the very least the Justice Secretary has to reassure the Scottish Parliament and the Scottish people that this situation has dramatically improved.”
Labour’s justice spokesman Daniel Johnson said: “The level of dysfunction in Police Scotland under Stephen House is well known, but allegations that rank and file officers had their concerns eradicated from reports to protect the top brass raise fundamental questions of integrity.
“Officers and the public need urgent and transparent reassurance about how this was allowed to happen - and who knew what and when.
“It is therefore essential SNP Justice Minister Michael Matheson give a statement to Parliament on these reports as soon as possible.”
Liam McArthur, the justice spokesman for the Scottish Liberal Democrats, also claimed the documentary was “set to leave a series of questions hanging over Scottish Ministers and police leadership”.
He stated: “The former Chief Constable is alleged to have whitewashed a critical report. It is essential, therefore, that the public is told whether current ministers and senior officers knew about the report’s existence and the level of interference.
“Liberal Democrats have repeatedly exposed problems arising from the SNP’s botched centralisation of policing.
“It seems that while SNP Ministers were insisting there was nothing to see here, someone was hitting the delete button.”
A Scottish Government spokesman said: “The Scottish Police Authority are seeking assurances from Police Scotland that matters raised were dealt with at the time. Clearly any specific allegations of misconduct should be dealt with by the appropriate authorities.
“The current leadership of Police Scotland and the Scottish Police Authority have made very clear commitments to improvement, including recent changes to how conduct and complaints issues are handled, while officers and support staff continue to work hard to keep our communities safe, having contributed to a fall of over 38% in recorded crime over the last decade.
“This is supported by the Scottish Government providing real terms protection to the police resource budget and a commitment to protecting the police resource budget - a boost of £100 million by 2021.”