Scotland's coronavirus guidelines could be enforced by new laws if "even a minority" continue to flout them, Nicola Sturgeon has said.
The first minister relaxed restrictions north of the border on Friday, allowing more people to meet up while outdoors.
She said the "vast majority" had complied with recommendations not to travel and to keep gatherings small.
But Ms Sturgeon said it was clear that not everyone had complied, with police dispersing more than 2,000 gatherings.
Police Scotland said there had been 1,391 "compliant dispersals" of groups of people over Friday, Saturday and Sunday, with another 650 where groups broke up "after a police warning".
And with car traffic trebling at some beauty spots, the first minister said she would not hesitate to put restrictions on group size and travel distance into law.
Scotland took its first step on the government's "routemap" out of lockdown over the weekend, with people from two different households allowed to meet up outdoors in groups of no more than eight.
People are also allowed to travel within their local area for recreation and exercise, although the government "strongly recommends" they do not travel more than five miles.
Ms Sturgeon said she wanted to thank "the vast majority" of people for sticking to the rules.
But she said it was clear that not everybody was heeding the advice, with police having to move on hundreds of people for not complying with regulations.
She said the 797 dispersals carried out by police on Saturday was five times the number seen a week previously, and that traffic volumes had risen sharply.
Traffic around beauty spots like Loch Lomond and Glen Coe was "about three times higher" than it was the previous weekend, with Ms Sturgeon saying it was "hard to see how that was caused by local residents".
She said ministers had "deliberately allowed some flexibility" and "left some room for discretion" when setting out the new guidelines, because they trusted the majority to follow the rules.
But she said: "It's worth being clear that if there is continued evidence of even a minority not abiding by these guidelines and travelling unnecessarily, or meeting up in larger groups, we will have to put these restrictions on group size and travel distance into law.
"We will not hesitate to do that if it is necessary for the collective wellbeing of society."
Police said more than 2,000 gatherings had been broke up in total over the weekend.
A total of 16 fixed penalty notice fines were issued, but there were no arrests related to breaches of coronavirus legislation.
Deputy Chief Constable Will Kerr said the "increase in people out and about following the relaxing of some of the restrictions has seen a rise in crime levels", with increasing demands on police.
He added: "We all want to enjoy our outdoor spaces safely and, whilst our officers will continue to robustly tackle crime and anti-social behaviour, please take reasonable steps to keep yourself safe and act responsibly."
The number of people in hospital with Covid-19 in Scotland continues to fall, with just 27 now in intensive care wards.
However, Ms Sturgeon warned that the progress which had been made was "fragile".
"The virus is being suppressed, but it has not gone away and it is still extremely dangerous," she said.
"The progress we have made so far is simply not guaranteed and is not irreversible. Cases could increase again, it would not take much for that to happen, and that would result in more loss of life.
"If all of that happens, then restrictions will have to be re-imposed rather than being further relaxed."
The first minister added: "To the minority that flout all of this, it's not just the virus running out of control you're risking - it's taking flexibility away from people who are abiding by the rules."
Ms Sturgeon said the issue had been brought home to her after one of her own friends had been diagnosed with Covid-19.
She said: "Until this weekend, I didn't know anybody personally, within my own family or friends network, who had had this virus in a significant way. That changed this weekend.
"Why am I telling you that? Because it's still there. Even with these numbers going down, there are still people testing positive for this virus.
"It's still there - it's ready to pounce, and jump across any bridges we offer it. If we want to stop that, we must, must stick to these guidelines.
"I'm saying this as a citizen as much as as a first minister - please do that, and together we will continue to make this progress."