Wales looks set to follow England in allowing fully vaccinated travellers from the EU and US to travel into the country without isolating.
First Minister Mark Drakeford said it would be “very hard” not to do so.
But he called for more detail on how the UK government will ensure the vaccine status of visitors.
The changes in England will come into force at 04:00 BST on Monday. The UK government said it will help to reunite family and friends.
Each UK nation sets its own Covid international travel rules, but Welsh ministers have implemented the UK government approach for a while.
The Welsh government earlier this month agreed to allow double vaccinated people to travel to amber list countries without isolating on their return.
But Mr Drakeford said at the time that he “deeply” regretted the UK government decision and to set a different policy would have been “untenable”.
Speaking on the BBC News Channel, the Welsh Labour leader said he would have preferred a more precautionary approach by the UK government, and said international travel was still best avoided.
It was “very hard for us not to follow suit”, he said.
“Most of those visitors arriving in the United Kingdom won’t be arriving through Welsh ports or our Cardiff Airport, they will be arriving at destinations in England or in Scotland.
“Once they’re in the United Kingdom, then they will be able to travel wherever they choose.”
Mr Drakeford said there was “practical detail that we don’t yet have available to us and we will need to see to make sure that we are confident… that that has been done properly and reliably, and to the sort of standards we would expect”.
The first minister added he was “reassured that the UK government is saying that the vaccines would have to be ones recognised by our own regulatory authorities”.
But he added: “The United States for example, there are no vaccine certificates, as I understand it.
“So, how will the UK government know that somebody travelling from the United States has been doubly vaccinated?”
He Mr Drakeford said: “It’s very important that the UK government is able to offer assurances that the risks that will be run – and there are risks whenever people visit from other parts of the world where the virus is in circulation, and where new variants of the disease may be emerging – that the proper precautions are in place to continue to defend the population of the United Kingdom.”
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