It also called for more to be done to help very small businesses participate in the apprenticeship system.
Micro firms in particular struggle with the administrative burden of setting up apprenticeships, organising training and securing financial support, the FSB claimed. To tackle the problem, funds from the government's skills budget in England should be ring-fenced for those hardest to reach, smallest businesses that do not currently benefit from the funding or even know it exists.
Additionally, a national Group Apprenticeship Programme needs to be set up to link potential apprentices with firms looking for a trainee. The programme would find apprentices jobs and place them in employment, while also taking on the administrative burden for small firms.
John Wright, the FSB's national chairman, said: "The majority of small firms would like to take on an apprentice but are put off by the administration involved, and the lack of financial support.
"In a survey of our members, 82 per cent said they would be in favour of an increase in the minimum wage for apprentices, which would give them more of an incentive to complete the traineeship and give employers a higher chance of serious applicants for the position. Small businesses are eager to do their bit and to take on new employees, but the government must step up and help them to tackle the problem of unemployment."
Pay apprentices more, urges business group.