Parents whose children play truant should have their benefits docked, Michael Gove has suggested.
The Tory Cabinet minister said the government could revive plans to penalise families in a drive to improve school attendance.
But teaching unions said targeting benefit payments would be counter-productive and just end up hurting children.
Mr Gove said the idea was originally considered by the coalition government under David Cameron but was blocked by the Liberal Democrats.
The Levelling Up Secretary suggested that it could now be re-considered as part of a move to restore "an ethic of responsibility".
Asked how the government could tackle anti-social behaviour at an event organised by the Onward think tank, Mr Gove said he believed it was important to ensure pupils were in school.
"We need to - particularly after Covid - get back to an absolute rigorous focus on school attendance, on supporting children to be in school," he said.
"It is often the case that it is truanting or persistent absenteeism that leads to involvement in anti-social behaviour.
“So one of the ideas that we floated in the coalition years, which the Liberal Democrats rejected, is the idea that if children are persistently absent then child benefit should be stopped.
“I think what we do need to do is to think radically about restoring an ethic of responsibility."
But the headteachers’ union warned that families needed to be offered help rather than threatened with losing benefits.
Paul Whiteman, general secretary of the NAHT, said: "Not only is this wrong, it is also likely to be counter-productive.
“It is very hard to see how consigning children to poverty and starvation will improve their school attendance. School staff are already deeply concerned by how many children are living in poverty and the impact that has on their academic performance and wellbeing.
“Persistent absence can only be successfully tackled by offering help, not punishment. What is needed are more support services and resources for schools to work with families and to refer to when there are issues."
Mr Cameron first spoke of the idea of cutting benefits for parents of regular truants in September 2011 when Mr Gove was education secretary.
He suggested it again four years later after the Tories won a majority.
At present parents can be fined £60 if their children are missing from school without a good reason, which rises to £120 if it is not paid within 21 days.
Those who fail to pay within 28 days can be subject to prosecution, but many parents do not end up in court because councils do not take legal action.
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