The UK should "build walls higher" to stop new variants entering the country, Wales' First Minister Mark Drakeford has said.
As part of England's roadmap out of lockdown, the UK Government has said international travel could resume no earlier than 17 May.
But Welsh and UK Labour leaders say it is too soon. Sir Keir Starmer said not enough had been done to secure borders.
Boris Johnson says the current system is among the toughest in the world.
Welsh Conservative Senedd leader Andrew RT Davies called Mr Drakeford's comments "Trump-esque".
The two Labour politicians made the comments in a joint virtual event on Monday.
It comes as health officials in England attempt to trace one person who has been infected with a concerning coronavirus variant first found in Brazil.
It is one of six cases of the P1 variant found in the UK in February.
Travellers to England from 33 countries have been required to quarantine in hotels for 10 days, since earlier last month.
Wales has adopted the same rules as England, while in Scotland the rule applies to international travellers from all countries.
Sir Keir said the search for the individual in England infected with a variant first found in Brazil "demonstrates the slowness of the government to close off even the major routes, but also the unwillingness to confront the fact that the virus doesn't travel by direct flights".
"I still think we have not secured our borders in the way that we should have done and the sooner that's done the better."
Mr Drakeford said the mid-May travel date "worries me hugely".
Wales saw a "big importation" of virus last September when people returned from foreign holidays, he said.
"I would build the walls higher for now against the risk that we would bring in to this country the variants that could brewing in any part of the world and could then put at risk all the careful work that we have done to try to keep Wales safe."
Later, at a press conference Mr Drakeford said Cardiff Airport, which is owned by the Welsh Government, would not take any flights from countries on the so-called "red list".
He said he would have the policy "the opposite way to the UK Government".
"I would say we shouldn't be having international travel, but here is a list of countries where we are confident that things are under control".
Prime Minister Boris Johnson defended the UK Government's measures on Monday.
"We have got one of the toughest border regimes anywhere in the world for stopping people coming in to this country who may have variants of concern," he said.
He said the government had moved "as fast as we could" with introducing hotel quarantine measures, describing it as a "very tough regime".
Andrew RT Davies told BBC Wales the first minister was "full of hot air".
'Not time for travel'
"Let's not forget back last June when Ryanair were flying flights in [to Cardiff] from Faro and Malaga," he said, adding "all" the Welsh Government had done in response was "write a letter".
Plaid Cymru's Helen Mary Jones agreed with the first minister that "this was not the time for international travel" and said restrictions should remain tight for the time being.
A UK Government spokesman said: "We continue to take every necessary step to protect the public and prevent the spread of the virus, including the stringent border measures currently in place.
"The reformed Global Travel Taskforce will assess how we can safely facilitate international travel when the time is right and while managing the risk of imported cases and variants."