A five-mile travel restriction could disrupt public trust in police, a leading officer warned.
Deputy chief constable Will Kerr sounded caution on the coronavirus guidance becoming strict law, hoping Scots will use "good judgement" to stay safe.
It follows a warning on Monday from First Minister Nicola Sturgeon after the first weekend of relaxed rules as Scotland takes the first steps out of "lockdown".
Sturgeon said it was "clear" some people ignored the remaining guidelines - particularly when it came to travelling long distances for recreation or visiting popular beauty spots. It was suggested the five-mile guidance could be written into law.
Today, Kerr sounded caution on adding more powers to police.
"People in Scotland don't carry identity cards so sometimes there will be no practical way to enforce some very necessary measures for public health without being overly intrusive," he told BBC Radio Scotland.
Asked if a five-mile law might damage trust in police, Kerr said: "It could potentially, if we have to be overly intrusive. But again, we are an operationally independent police service.
"We will make decisions about how we operationalise the law that our government and politicians give use - that's the right and proper order of things.
"But the collective and individual responsibility on us all is to follow the legislation and the guidance to save lives."
Kerr said a blanket travel restriction would cause problems for people in more rural areas who need to travel greater distance.
Police Scotland issued 797 dispersal orders across the country on Saturday - five times the number given out the week before - while transport usage was up 60 per cent.