Gordon Brown, announcing the training posts at a Cabinet meeting in Southampton during national Apprenticeship Week, said the total would include 5,000 apprentices in the NHS, 7,500 in local government and 4,500 in schools and children's services.
However, officials later acknowledged that many of them would involve adding a training element to existing roles, and any new jobs would depend on organisations' normal turnover and vacancy rate.
During the Commons debate on the Apprenticeships, Skills, Children and Learning Bill, Ed Balls, the Schools Secretary, was challenged by David Willetts, the Conservative shadow skills secretary, about whether the apprentices represent new training and new jobs.
Mr Balls said: "I am happy to give that assurance. These are new apprenticeships in the public sector, and there will be 21,000 more of them from the 35,000 that we are going to deliver with pound;150 million worth of spending."
However, a spokeswoman for the Department for Innovation, Universities and Skills clarified that there was no requirement to create new jobs and it could not know whether the apprentices would be created from existing roles.
"Many apprentices in both the public and private sector are in jobs before they begin their apprenticeship and that's perfectly acceptable," she said. "They are not only about getting into work but about progression in your job and getting a valuable qualification."
The department believes it might not be fair for employers to offer training to external candidates that was not available to internal ones. It also determined that its apprenticeship scheme must be about training, rather than creating jobs which could not otherwise be justified.
In a further announcement this week, the Government responded positively to appeals from training providers to do more for apprentices who were made redundant before completing their training. In future, apprentices will be able to continue their off-the-job, full-time training for up to six months after redundancy.
A Dius spokeswoman said: "This will allow redundant apprentices to maintain their framework for an extended period while they and their (training) provider seek a new employer, and reflects the greater challenge faced in finding a new place in the current economic climate."
The spokeswoman emphasised that the six-month period of funded provision was not offered in place of employment but as a grace period while apprentices looked for a new employer. The extended funding was for training, not wages, she explained.
The announcement follows an appeal by the Association of Learning Providers for greater flexibility over apprenticeships. In a letter to the Prime Minister last month, Graham Hoyle, the association's chief executive, called for training allowances to be paid to employers, allowing them to retain apprentices earmarked for redundancy.
Meanwhile, the results of a survey of 500 employers in January by Populus on behalf of the Learning and Skills Council, released to mark national Apprenticeship Week, show that eight out of ten employers believed apprentices had helped them improve their companies' productivity.
WHAT EMPLOYERS THINK OF APPRENTICES Source: Populus survey for the Learning and Skills Council.
Source: Populus survey for the Learning and Skills Council.