Government plans to expand parenting classes to help foster a "culture of respect" must be properly funded, head teachers have warned.
Ministers want to ensure parents "fulfil their responsibilities" and are offering allowances to teenage parents if they sign up for classes.
There are also plans to set up a new national parenting academy to train professionals on giving advice.
Services will be offered at children's centres and through extended schools.
Head teachers representatives said schools would welcome involvement in the "respect agenda", if it was properly funded.
General secretary of the National Association of Head Teachers, Mick Brookes, said: "The notion of parenting classes is a very important one.
"Whilst a lot of parents are fairly good, there is a large minority who don't know how to parent their children and they are crying out for help," said Mr Brookes.
"But this can't be another thing that's loaded on the backs of schools.
"Any new initiative needs to be carefully thought out and, if schools are to deliver it, there must be proper financial support to enable schools to do that."
Mr Brookes said teachers were very likely to want to "enter the arena" of parenting classes and stood to gain if pupils' behaviour improved as a result.
John Dunford, general secretary of the Association of School and College Leaders (formerly the Secondary Heads Association), said schools had been working for many years to promote respect.
"For schools this is not a new agenda," said Dr Dunford.
"In many cases it is an uphill struggle against popular culture and mainstream society," he said.
"Schools need all adults, including politicians, pop stars and footballers, to back them up by modelling good behaviour in order to make a difference.
"We welcome the prime minister's support for schools in doing this, in particular, by reminding parents that they have responsibilities as well as their rights."
Philip Parkin, General secretary of the Professional Association of Teachers, welcomed the government's committment to supporting families with parenting problems.
"All too often schools get the blame for poor pupil behaviour, but children need to arrive at school ready and willing to learn.
"Their mental and physical preparation, and their attitudes to teachers and fellow pupils, begin at home."