Officers want to be trusted to enter the properties where important evidence may be hidden without giving up vital time which helps potential criminals evade justice.
The group that represents police superintendents claims stolen property, drugs and firearms are being destroyed or removed by suspects before officers can gain entry.
The Association of Scottish Police Superintendents (ASPS) said its officers were often left in the position where they believed a serious crime suspect was within a property but were unable to arrest them without first seeking a search warrant. It wants practices to be brought into line with south of the Border, where police have been able to issue warrants since 1984.
The body's president, Chief Superintendent David O'Connor, said: "During the procedural delay to follow current criminal justice processes there is scope for evidence to be disposed of, stolen property or a firearm to be moved and never recovered, harmful controlled drugs to be either destroyed to avoid prosecution or transported to other locations.
"This cannot be in the best interests of victims of crime or the law abiding majority of the public."
Human rights lawyer John Scott, QC, branded the move "irresponsible" and warned police already had the necessary powers to ensure evidence was not destroyed or removed from properties.
He said: "They're asking for more powers and less scrutiny. It's entirely appropriate there be judicial oversight of what they do in terms of searching property and it can be done quickly. Even without a search warrant police can already secure a property in serious cases if they think evidence is going to be destroyed."
Mr Scott added: "If you reduce the scrutiny, you open the police up to increased allegations and open innocent people up to improper activity on the part of the police."
The ASPS made the call in a submission to the Scottish Government as part of its response to a consultation on the reform of Scots Criminal Law and Practice.
In order to be able to search a private property, police must either have the consent of the occupant or seek authority from a procurator-fiscal to appear before a justice of the peace or sheriff and apply for the warrant under oath.
Mr O'Connor added: "We hope the opportunity will be taken to provide police in Scotland with powers that have been available elsewhere in the UK for over 25 years and remove a barrier criminals can hide behind while a warrant application is made and a warrant obtained."
He said the warrants would only be issued when a suspect had been arrested and officers wanted to search his or her property or when police wanted to make a specific arrest, and would not be used for "fishing trips". Mr O'Connor added that, as a safeguard, the search warrants would only be issued by a senior officer who had no links to the investigation.
However, Mr Scott warned that even if the role of issuing search warrants was only given to senior officers, it could simply become a "rubber-stamp exercise".
The ASPS argued that police "cannot possibly provide the resources" to secure all premises while warrants were sought.
Mr Scott said this was then "an argument for more manpower, not more power".
A Scottish Government spokeswoman said the submission would be considered along with others received, adding: "The Government is keen to consider what further changes could be made to make the process for warrants simpler and more efficient. We are always happy to listen to views on how to improve the criminal justice system."
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