The idea of a legal extension of the school day once a week is contained in a report by the influential Institute for Public Policy Research. Parents who do not make sure their children take part could be fined, the left-leaning think tank suggested.
Analysis of research on binge drinking, drug use, under-age sex and vandalism, given in the same report, recently led to media coverage branding Britain's teenagers "the worst behaved in Europe".
Mick Brookes, the general secretary of the National Association of Head Teachers, said: "We need to get away from these threats. Putting children in a kind of prison once a week will not go down well with my colleagues.
"Who is going to take these sessions? Why would anyone want to do it?
"What we need in schools is a culture where kids know what they're doing is valuable. There has to be a reason for them to stay at school."
Mr Brookes said that headteachers would be disappointed by the "naming and blaming" of the nation's teenagers.
"The report is simplistic," said John Dunford, the general secretary of the Association of School and College Leaders. "There is no relationship between the length of time spent at school and the quality of education.
"It is very unwise to be tempted by the idea of compulsion. This would create a whole new set of problems. It would be far better to use the opportunity of extended schools to encourage young people to take advantage of what is on offer."
Nick Pearce, the director of the institute, said the shift to a service economy in Britain meant that children needed social skills, as well as traditional qualifications.
He said that structured activities after school, such as the cadets, martial arts and drama clubs, were the best way for children to learn skills such as communication, planning and self-control.