Fines issued to people who break coronavirus lockdown rules need to be greater, Dyfed-Powys's police and crime commissioner has said.
Dafydd Llywelyn said current penalties "aren't enough of a deterrent".
People found to be breaking the rules can be fined £60, although this is reduced to £30 if paid within 14 days.
On Friday, First Minister Mark Drakeford said he would be prepared to look at the issue if asked to do so by police forces.
Mr Llywelyn told BBC Radio Cymru: "I'm calling personally for the fines given to people to be bigger because I don't think the current guidelines the police have are a great deterrent."
Despite repeated warnings not to travel over the Easter the weekend, many people had been arriving in the force area, which covers Ceredigion, Carmarthenshire, Pembrokeshire and Powys, Mr Llywelyn said.
It’s just gone midnight and we’re conducting checks on the A477 at St. Clears. The first car stopped is from Manchester, over 200 miles away, the driver states he is going to Ireland to collect a dog. He is turned around and reported, he states he knew he was ‘chancing his luck’. pic.twitter.com/iyXrPulbfO— Pembrokeshire RPU 🏴 (@PembsRPU) April 11, 2020
He said the force had issued about 250 penalty notices, but said people "aren't listening".
On Friday evening, the Pembrokeshire Roads Policing Unit, which is part of the Dyfed-Powys force, tweeted to say it had stopped a man who had driven from Manchester to pick up a dog from Ireland, and a car from Cardiff carrying cockle picking equipment.
The Welsh Government said: "The vast majority of people are following the stay-at-home rules and we thank them for their ongoing cooperation and help.
"We have regular discussions with the police. If they say they need more powers, they will get them. If the penalties are not sufficient, we will look at them again."
It’s 1am, a vehicle from Cardiff is stopped at Llanteg. The occupants say they’re off to Tenby to collect rice from a friend, however the postcode leads to a beach. The driver opened the boot, within were items linked to cockle picking. Occupants reported & escorted out of Pembs. pic.twitter.com/5lpqyfHaRQ— Pembrokeshire RPU 🏴 (@PembsRPU) April 11, 2020
The Plaid Cymru police and crime commissioner is also concerned about a "loophole" which makes it difficult to take action against second home owners once they have arrived.
The first minister suggested on Friday the Welsh Government could look at taking action in relation to the use of second homes as the pandemic continues.
He also said that should the police request greater powers, "they will get those powers".
"If they think that the penalties are not sufficient we will look at the penalties as well," he said.