Paul Whiteman, general secretary of the National Association of Head Teachers (NAHT) said non-attendance can mean children miss important learning.
But, he said the use of fines to manage absence “increasingly appears to be an overly simplistic solution to a more complex issue, and it is becoming clear that this approach is increasingly ineffective.”
Pepe Di’Iasio, general secretary of the Association of School and College Leaders, said there was “good evidence that missing time in the classroom has a direct impact on a child’s attainment and future prospects”.
But he said it was “clear that fines are not acting as much of a deterrent”.
A spokesperson for the DfE said: “We’re determined to give children growing up in our country the best start in life. But that can only happen if children regularly attend school.
“We have already made significant progress with five million more days in school last academic year and 140,000 fewer pupils persistently absent.
“Term time holidays place the burden on teachers to support missed learning – affecting the entire class. That’s why fines have a vital place in our system, so everyone is held accountable for ensuring our children are in school.”
Additional reporting by Jonathan Fagg, Ema Sabljak and Lauren Woodhead