Activists have vowed to “keep challenging” the limitation after a meeting of the local authority’s education committee yesterday.
Pupils had previously been turning up to protest outside the Scottish Parliament on an “ad hoc” basis, with permission first granted by the council in March.
It was the first council in Scotland to make such a move. Now absences to protest that are not part of the agreed day off during the academic year will be recorded as unauthorised, with “parental consent” required.
Eight councillors voted for the motion, while two Greens voted against.
More action is planned by the Scottish Youth Climate Strike (SYCS) group on September 20 and 27 as part of what has become a global movement started by 16-year-old Greta Thunberg. Sandy Boyd, of SYCS, said after the meeting: “It’s a little disappointing but they have given us permission for one strike a year.
“We will keep striking no matter what and we will keep challenging the council on this.”
Thousands of children descended on the Scottish Parliament in March and May along with fellow pupils in more than 100 towns and cities across the UK.
Smaller groups have been gathering at Holyrood every Friday since January.
Edinburgh council education convener Ian Perry said: “We support the young people making their voices heard regarding climate change as it is one of the most important issues that’s facing the world. However, there needs to be a balance struck and if we allow pupils more than one absence the issue is that they could be regularly missing school which affects their education.
“We are also encouraging schools to support pupils in any projects which help educate them in school about climate change.”
Lorna Sweeney, the council’s schools and lifelong learning senior manager, said: “Fundamentally we have to make sure the children attend.
“If we give conflicting information to parents it makes the whole purpose of education very difficult. The principle purpose of schools is to raise attainment. The single biggest factor is attendance.”
Edinburgh councillor Callum Laidlaw, Conservative education spokesman, backed the decision to limit the authorised strike action to one day.
He said: “There are consequences of missing school and we have a duty of care. A strike is not a strike because it’s authorised – it becomes a day off.”
Green councillors called for the proposals to be halted.
Steve Burgess said: “To place an arbitrary limit on it at this stage does not appear to be responding appropriately to young people.
“Let’s keep an open mind and do it on a case-by-case basis.”