There are no general teacher shortages in the principality, said Jane Davidson, Welsh education minister, adding that a crisis seemed unlikely.
"I am not aware of any school in Wales that has indicated it could introduce a four-day week," she wrote in a combative article in the Western Mail last week.
But the National Union of Teachers Cymru said schools in Wales faced a "silent but growing crisis".
The union said shortages in Welsh secondary schools were being concealed by staff teaching subjects in which they were not trained.
And NUT Cymru secretary Gethin Lewis said ageing staff would cause a crisis in the future by retiring all at once.
Figures for January last year showed there were just 42 vacancies at secondary level and 26 at primary across the whole of Wales.
Wih a Welsh teacher workforce of more than 27,000, that means a vacancy rate of only 0.3 per cent (compared with 0.7 per cent in England and 2.3 per cent in inner London).
Of the 22 Welsh local education authorities, 10 recorded no vacancies and the worst-hit only 15.
So why isn't Wales generally short of staff? John Andrews, chairman of the General Teaching Council for Wales, said the profession probably remained a more popular career choice because teachers were more respected. And there were fewer areas like London where teachers were reluctant to go.
But he too expressed concern about reports from secondary schools that staff were having to teach subjects for which they were not trained.
Teachers trained in biology, for instance, were probably able to teach chemistry but physics would be "much more difficult", said Professor Andrews.
He said the council was investigating the problem but it had only anecdotal evidence at present.