The National Association of Head Teachers (NAHT) also urged stern action against children who are continually late and said that it would back moves towards cutting child benefit from those parents who encouraged their children not to attend school.
David Hart, general secretary of the NAHT, said that lateness for lessons and children being taken out of school for holidays eroded discipline and encouraged truancy. A union submission to ministers argues that both can foster a "lax attitude" to attending school.
Heads say it is essential to convince parents that "truancy equals poor results, leading to unemployment, crime and a wasted life". Estimates suggest that as many as a million children play truant at some time. Some are as young as seven.
Headteachers are hoping the Prime Minister's Social Exclusion Unit will back a hard line on truancy. The unit, set up to "think the unthinkable", is understood to have floated the idea of withdrawing child benefit as a way of bringing into line parents whose children play truant.
Mr Hart said that benefit cuts could be used as an alternative to prosecution in the rare cases where parents persistently fail to make sure their children go to school.
He said: "Parental duties must be tackled with as much vigour as parental rights. Far too often parents either connive at their children's truancy or fail to take seriously their children's exclusion from school."
He said new penalties should be considered to deal with what he called a hard core of parents who "actively encourage non-attendance".
From September, all parents and children will have to sign new home-school contracts, covering truancy, homework and general discipline.
But Mr Hart called for stronger action against parents who "arrogantly" take their children out of school. He said: "The Government must change the law and simply make it illegal for parents to take their children away from school during term time. That would send a strong message to parents that they are supposed to have their children at school."
Margaret Morrissey, spokeswoman for the National Association of Parent Teacher Associations, said parents would be helped if the heavy peak-time cost of travel was reduced. She said: "We really need to be getting together with the travel agents and all the people who make money out of parents at holiday time. We do not condone parents who take children out of school, but it can be understandable.
"What we would like to see is some support for parents who are failing to get their children to go to school."
The Government has committed pounds 21m to initiatives designed to reduce truancy. Parents who fail to ensure that their children attend school already face fines of up to pounds 1,000, but prosecutions are rare.
An Audit Commission study has shown that two-thirds of school-age offenders against the law are either excluded pupils or persistent truants.