A total of 25 fixed penalty notices have been issued in Scotland to people ignoring coronavirus regulations.
It is a criminal offence to breach the rules about social distancing aimed at tackling the spread of Covid-19.
Police Scotland dealt with a number of incidents over the weekend including house parties and groups of people gathered outdoors.
But a senior officer said the "vast majority" of people were complying with the rules.
Fines start at £30, doubling to £60 if they are not paid within 28 days. Repeat offenders can face fines of up to £960.
Deputy Chief Constable Malcolm Graham said there were issues with people driving to some outdoor spaces such as parks.
He told BBC Radio Scotland's Good Morning Scotland programme that it would take time for people to work out what was acceptable, especially with regard to outdoor exercise.
"It's such a significant change in everybody's lives," he said. "This was made very clear last week by the chief constable - we're going to do this through policing in Scotland as we always do."
He said that where officers had encountered people outside they have been able to speak people about the importance of the public health guidance.
But he added that sanctions were in place as a "last resort" for people who refused to change their behaviour.
"If there are repeated instances then the penalties rise very quickly and we'll see if that has an impact."
Concerns had been raised about the number of people using the most popular public spaces.
Strathclyde Park in Lanarkshire was busy with parked cars, although images appeared to show those on foot maintaining social distancing.
North Lanarkshire Council said: "We had already closed car parks, but we'll be ensuring vehicles can't access the park like this again, working with Police Scotland.
"Please be responsible. Driving to the park to exercise is against govt guidance and not responsible."
Mr Graham said incidents Police Scotland had dealt with included house parties and groups of people gathering outdoors.
"We've also received a significant number of calls, firstly from people asking how do we comply with these regulations and, secondly, reporting people they felt were breaching them," he said.
"We responded to those calls to make sure we could again explain why it was important, encourage people to comply with them, and in those very small number of occasions use the enforcement powers that we've got where that very small minority of people just refuse to comply with what is required."
He added that, in a small number of cases, fixed penalty notices had been issued to businesses which were operating in circumstances which were not appropriate.
In a statement later issued by Police Scotland, Mr Graham added: "We have been given extraordinary powers in an extraordinary situation, powers we would not normally wish to have, but I'd like to thank the public for helping and supporting us."