The revelations in The Herald about pressure on officers to "massage the figures" and participate in an "unethical culture" of stop-searches prompted the call for an investigation.
Tavish Scott of the Liberal Democrats said: "Our police work incredibly hard in hugely challenging circumstances. But officers know that their job needs to be far more than a box-ticking exercise. We need to get to the bottom of these serious allegations and an independent investigation is the way to do it. Officers need to have confidence they can report their concerns without fear of reprisals.
"We need to know where the pressure on officers is coming from. Ministers? The Chief Constable? I know that Holyrood's Justice Committee will want to look very closely indeed at these deeply concerning reports."
More than a dozen police officers have approached The Herald to express their concerns about issues such as pressure on divisions to meet specific targets and record "positive" stop-searches, which has led to some officers selecting people with alcohol outside off-licences and known methadone users leaving pharmacies.
Officers say some divisions now have league tables with those who conduct most stop-searches and catch most speeding motorists named at the top.
They claim such tables are used as "leverage" against those wanting promotion or career progression.
As a result, some frontline officers are conducting stop-searches without due cause and falsely recording "positives".
Labour justice spokesman Graeme Pearson, a former senior police officer who headed the Scottish Crime and Drug Enforcement Agency, also expressed grave concerns.
He said: "This insight into what is happening within the Police Scotland is extremely concerning and not what Scotland wants for a national police service.
"No doubt Mr [Cabinet Secretary for Justice Kenny] MacAskill will again steer clear of these matters claiming they reflect operational issues for the chief constable."
He added: "The truth is, however, policing should reflect the priorities set by the public as outlined by the Scottish Parliament.
"Thereafter Mr MacAskill should be busy ensuring the Police Authority play their part in delivering the service we seek rather than the one they would prefer. The absence of a real challenge to leadership in policing must change."
Margaret Mitchell, justice spokeswoman for the Scottish Conservatives, said: "There have always been concerns that officers are being put under unnecessary pressure to meet targets and now it has been confirmed.
"These officers are brave to speak out but it's unacceptable that they cannot do so without the fear of losing their job.
"It's clear Police Scotland are driven by targets rather than the protection of the public, and concentrating on collecting fines to fill their coffers is no real alternative to tackling crime."
The concerns have already been raised with Chief Constable Sir Stephen House by the chairman of the Scottish Police Federation, Brian Docherty, who was promised that action would be taken if bad practice was identified.
Deputy Chief Constable Rose Fitzpatrick said such practices would not be acceptable, but she defended the use of performance targets on key priorities reflecting public concern.