The Education Secretary Charles Clarke criticised Prince Charles as "old-fashioned" after he said the "learning culture" gave people hope beyond their capabilities.
The Prince of Wales sparked a debate
In a leaked memo, the Prince had complained about a "child-centred system which admits no failure".
Mr Clarke responded by saying it was very important that children were given ambition.
"We can't all be born to be king but we can all have a position where we really can aspire for ourselves and for our families to do the very best that we possibly can and I want to encourage that position," he said.
The comments have sparked an intense debate about the purpose of education - and its strengths and weaknesses - in the UK.
The former chief inspector of schools Chris Woodhead has been very critical of current standards and is understood to have had detailed discussions with the Prince of Wales.
He told BBC Breakfast there was nothing wrong with having ambition - as long as it was realistic and in line with a person's abilities.
"There is nothing wrong with encouraging children but it's wrong and cruel to deceive children with regard to their real abilities.
"The government wants 50% of 18 to 30-year-olds to go to university and there aren't the graduate-status jobs to go with it," he said.
"I'm all for raising expectation and encouragement but there also has to be a good dose of realism."
John Dunford, the general secretary of the Secondary Heads Association backs Charles Clarke's views.
"Prince Charles' views of the world are out of date and he should either ensure that he is well informed or keep quiet on the subject of state education, about which his family have little experience," he said.
"This is a Woodhead view of the world, which does not accord with modern reality."
Earlier this week, Prince Charles had complained that schools were turning out robots, rather than people with inquiring minds.
In a letter read at a conference of the Association of Colleges, he said "teaching and inspiration" had been replaced by "computer-driven modules" based on serving the needs of the economy.
John Brennan, chief executive of the Association of Colleges, seems to have some sympathy for the Prince's views - but only up to a point.
"Education and development is not simply about getting people to become robots but about helping them to be successful in the totality of their lives," he said.
"We have to encourage young people to be ambitious.
"There are elements of both views which I think are right, but what we need to do is find a different way of expressing this in order to help all our young people, not simply to take us into a sterile debate about whether we are too focused on economic issues or neglecting other aspects of young people's development."
The Confederation of British Industry (CBI) says it believes education is letting people down in some areas.
A spokesman said: "Employers are concerned that 50% of the young people they recruit do not have good basic skills in numeracy and literacy.
"A third of employers offer remedial training to compensate for failings in the education system.
"We don't want to get into a row over Prince Charles, but what business wants is youngsters who are literate, numerate and motivated to get on."