Youth climate strikers are to be given permission to take part in protests for one authorised school day per year.
However, Edinburgh councillors say no punishment will be levelled at pupils or parents if they choose to strike over a longer period.
The city council's education, children and families committee approved a motion by the SNP-Labour coalition to limit authorised absences to one day.
This was despite a plea from activists to back the pupils' action.
It follows two emergency motions by Green councillors earlier this year where pupils were allowed to attend climate emergency demonstrations with parental permission on a one-off basis.
However, officials warned that "potential for adverse risk to children who are absent and unsupervised is high and runs counter to child protection and raising attainment."
A report said "almost all head teachers were not in support of children's absence being authorised" by councillors as it had "devalued the hard work they had undertaken in working with parents who did not value good attendance at school".
Sandy Boyd, a youth climate activist from Trinity Academy, said the decision was "morally wrong".
He added: "The youth climate strike movement has brought change across the world.
"It will stop this progress dead in its tracks. You are trying to suppress young people's opinions on matters that will affect young people.
"We are imploring this council to allow us authorised absence to pressure governments - finally, we are seeing some action.
"The educational value of taking part in these events is massive. It's building a society that we want to see. We will keep doing them until we see change."
However, council officers highlighted the importance of ensuring that pupils attended lessons.
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 make the whole purpose of education very difficult.
"The principle purpose of schools is to raise attainment. The single biggest factor is attendance."
Andy Gray, head of schools and lifelong learning, said if pupils took part in strike action with parental permission, there would be no financial penalty.
He added: "We are not going to punish children for this activity but what we are saying is that it's definitely an unauthorised absence."
Councillors voted to limit the authorised strike action to one day.
Ian Perry, the council's education, children and families convener, said: "There's no doubt if I was at school I would be doing exactly what Sandy [Boyd] is doing.
"I think everybody recognises that movement is increasing and is having a big affect. Having said that, we have to remind people the duty of this education committee to provide the best education for the young people of this city to prepare them for life.
"We would then be saying that attendance at school is not important and we don't value it.
"I think in order to show solidarity with the climate movement, we should allow one day."
Callum Laidlaw, Conservative education spokesman backed the limit.
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."
However, Green councillors called for the proposals to be halted.
Steve Burgess, whose council ward covers Southside and Newington 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."
BBC Scotland News is running a season of climate change coverage across radio, TV, online and social media.