The Scottish Government announced on Tuesday, September 1 that passengers arriving from Greece would have to self-isolate for a fortnight as of Thursday, September 3.
Wales is asking arrivals from the island of Zante to begin the period of quarantine.
The Department for Transport said no change to its rules for England had been made, but Wales’ health minister Vaughan Gething said he would be pressing the UK Government for an urgent meeting to consider the potential risk in Greece.
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Restrictions for Greece were lifted in England in July when international exemptions were first permitted.
There were 14.0 coronavirus cases per 100,000 people in Greece in the seven days to Monday, August 31, down from 14.9 a week earlier.
A seven-day rate of 20 is the threshold above which the UK Government considers triggering quarantine conditions.
Mr Gething said six clusters amounting to more than 30 cases of Covid-19 in the last week had come from four flights, two of which landed in England.
“There are concerns from our public health teams that the current advice and control measures for returning travellers are insufficient,” he said.
He said that all passengers on a flight from Zante to Cardiff on Tuesday night would be told to quarantine and would be given two Covid-19 tests, one within 48 hours and another eight days after their return.
“In addition, I have pressed for an early meeting with the UK Government and devolved nations [on Wednesday] to consider the latest assessment of risk by the Joint Biosecurity Centre,” he added.
“There is an obvious need for us to consider the potential for changes to the regulations in Wales which would require travellers arriving in the UK from Greece and possibly elsewhere to self-isolate on their return.”
Tour operator Tui later said it would no longer be offering holidays to the resort of Laganas on Zante from Thursday.
The Joint Biosecurity Centre was yet to change the risk rating for Greece but the data for the nation, like all others, was being kept under constant review.