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Ministers are considering increasing fines for breaching travel restrictions in Wales after reports of visitors flouting lockdown laws at the weekend.
First Minister Mark Drakeford said he will raise the level of fines if police figures show the current system is not "effective".
Wales has not followed England in allowing people to drive for exercise.
But fines in Wales are lower - £60 for a first offence compared to £100 for England.
Police forces have called for the fines in Wales to be increased to the same level.
Dyfed-Powys Police and Crime Commissioner, Plaid Cymru's Dafydd Llewellyn, said the difference in fines was "perverse", when Wales has stricter guidelines but lower sanctions.
He said police were noticing public spaces becoming increasingly busy.
"We've seen it incrementally getting busier since the lockdown went into force at the beginning of it and we're expecting that that will continue as the lockdown is eased," he added.
Dyfed-Powys has issued the largest number of fixed penalty notices for lockdown in Wales, at 417.
Figures between 27 March and 11 May show only 799 fines have been issued, with 157 by South Wales Police, 143 by North Wales Police, 71 by Gwent and 11 by the British Transport Police.
At the weekend North Wales Police reported turning around tourists from Manchester, Norwich and London as they tried to visit parts of Snowdonia.
Drivers from Bristol and Wolverhampton were fined for heading to Stackpole, Pembrokeshire, along with a Birmingham family in the Brecon Beacons.
Mr Drakeford told BBC Radio Wales Breakfast that he will receive his weekly report from Wales' four chief constables on Monday morning "to see what happened over the weekend".
"If we find that there has been an increase in people coming across our border... doing it recklessly, then that conversation about the level of fines with our chief constables and police and crime commissioners will continue at the start of this week."
Mr Drakeford said he will find out if the fines "are doing the job already".
"If they're not being effective, and the way to make them effective is to raise the level, then that's what we will do," he added.
Under the law governing lockdown, the police can issue fixed penalty notices ranging from £60 for a first offence to £120 for subsequent offences.
First offence fines fall to £30 if paid quickly.