Parents should be allowed to take their children on term-time holidays without being threatened with fines or arrest, according to council chiefs.
The Local Government Association said headteachers should turn a blind eye and refuse to tell local authorities when families take children on holiday during term-time so that they can take advantage of lower prices.
At the moment, if an absence is not authorised, local authorities have an obligation to fine parents and enforce legal proceedings on behalf of schools.
Under the current system, parents who take children out of school without permission could face a £60 fine per child, rising to £120 if it is not paid within 21 days.
Those who fail to pay can face prosecution, with a maximum fine - if convicted - of £2,500 or a jail sentence of up to three months.
The controversial rules on term-time trips were introduced last year by Michael Gove, the former Education Secretary.
They effectively penalise some families who are unable to afford to take breaks during school holidays because companies put up prices to take advantage of parents.
Previously, school leaders could grant up to 10 days leave a year for family holidays in special circumstances.
The LGA said that while it supported the Government's view that every child should be in school every day, it believed there were occasions where parents' requests should be considered - such as religious festivals, weddings, funerals or a 'once-in-a-lifetime opportunity'.
A spokesman for the LGA said: "We are asking for headteachers to be given the discretion to allow parents to take children out of school, as was the case with the ten day discretion period up until September 2013, when these new rules came into play.
"We fully support that children should be in school every day, but there are occasions such as religious festivals, weddings, funerals or perhaps a once-in-a-lifetime opportunity whereby parental requests should be given individual consideration.
"Headteachers, who know the families and individual circumstances, should be allowed to make that decision, not government."
However, Brian Lightman, general secretary of the Association of School and College Leaders, said: "There is already the flexibility to allow children to miss school for 'exceptional circumstances' such as a family wedding or once-in-a-lifetime opportunity, but these should be extraordinary and rare.
"We sympathise with parents' plight, but the way to address this problem is to tackle the holiday companies that charge extortionate fees, not to allow more children to miss out on school. In this case we agree with the Department for Education completely."
Figures published earlier this month showed that 2.5 million school days were lost because of family holidays in the autumn and spring terms of the last year, down 0.8 million from 3.3 million the year before.
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