Greater numbers of people breaking lockdown rules in urban areas of Wales
The First Minister said there have been more people breaking lockdown rules in urban areas than rural areas over the weekend.
Mark Drakeford AM said the police forces in Wales told him there have been examples of "increased activity" across the whole of Wales but mostly in towns and cities.
Mr Drakeford added: "My message is to people who think a journey to Wales is a sensible use of their time, it is not.
"Police have powers to stop them, turn them back and fine them. Now is not the time.
"I do understand what an ask we are making of people at this time but we cannot see these measures slacken."
On Saturday, a group of people appeared to be ignoring lockdown measures by travelling on horse and cart through Roath Park in Cardiff.
Police have been regularly patrolling the area and officers ordered the group to leave the park and return to their homes.
Although the majority of reports of lockdown rules being broken have been in urban areas, some still attempted to visit Snowdonia this weekend.
The Chief Constable of North Wales Police, Carl Foulkes, said: "We're seeing the vast majority of people in North Wales staying home and staying safe but we have seen a slight increase of road traffic and we've also seen more people out and about."
Chief Constable Carl Foulkes said those who travelled to Snowdonia were escorted out of Wales.
He said, "The figures over the weekend when we went over 20,000 people that tragically lost their lives, if anybody needs to measure out why they need to do the right thing, that is the strongest measure I can give around, please stay home, stay safe and support the NHS."