Wales First Minister Mark Drakeford says he was not consulted before the UK government altered the lockdown slogan from “Stay at home” to “Stay alert”.
He told the BBC’s Nick Robinson he did not think it was the “right time” to change to the new message, adopted in England but not elsewhere in the UK.
Meetings with London had come in “fits and starts” during the coronavirus crisis.
He was speaking to the Political Thinking with Nick Robinson podcast.
It came as the Welsh government unveiled cautious plans for easing the coronavirus lockdown.
Prime Minister Boris Johnson announced the use of the slogan “Stay alert. Control the virus. Save lives” on Sunday.
It has been criticised as too vague, but Mr Johnson insisted it was “absolutely right” for the current situation, in which social distancing has to be maintained while restrictions ease.
Wales, Scotland and Northern Ireland – which, unlike England, have not freed up road travel and removed limits on outdoor exercise – have chosen to stick to the “Stay at home” message instead.
Mr Drakeford told Nick Robinson: “We heard about the (‘Stay alert’) slogan after the decision had been made and had to make it clear that what we heard didn’t persuade us that this was the right time to change the slogan or that was the right slogan to change to.
“Had we had more regular, reliable engagement we might have had better chances to talk those things through.”
Mr Drakeford, a Labour politician, added that there had not been a “regular rhythm” to meetings between the UK government and the devolved administrations during the coronavirus crisis.
They tended to “come and go” and take place in “fits and starts”, he said. adding: “Had we had, over the three weeks that led up to last weekend, a regular and reliable pattern of meetings between us, I think we would have a better chance to have avoided the rough edges that we ended up in.
“What we had was two weeks with no meetings at all and a final week where everybody’s under the pressure to make decisions and get things done, a sudden rash of meetings on Wednesday, Thursday, Friday and Sunday.”
The UK government wants some children to begin returning to primary schools in England by June.
But Mr Drakeford said schools in Wales would “not reopen for new cohorts of children” at that point.
He added: “We still have ambitions to have more children returning to school before the end of the [summer] holiday but you’ve got to do it in a way that convinces parents and teachers that it is safe for them to do it.”
The UK government’s communities secretary, Robert Jenrick, has defended “Stay alert”, calling it a “cautious” slogan for a time at which rate of coronavirus infection remained high and the public were “understandably anxious”.
He added: “The public are capable of understanding a broader message as we move into the next phase of the virus.”