However, a majority of councillors did support paying up to $5000 towards the consent costs.
Council chief executive Ross McNeil said the school's position was that the trees presented a significant safety risk.
However a council commissioned independent assessment of the trees found there was a "reasonably low risk" of tree canopy failure.
"There is a management regime that can be applied to maintain the health and status of the trees and minimise risk," Mr McNeil said.
"Essentially the decision council will have to make is around the extent to which council believe those trees represent imminent danger to health based on the information available."
There was little support for that but there was support to help the school keep and manage the trees, led by councillor Tim Harris.
"I'd hate to see them destroyed. It's crazy. Let the trees grow, they've been there for 100 years," he said.
"There's just as much chance of a child getting run over on the road. I'd be up in arms if they were cut down."
Mr Harris said he was happy to help the school find sponsorship to maintain them.
Councillor Cath Ash said the advice council received did not support classing the trees a threat.
"Everything in the report suggests that the health of the trees can be enhanced with actually looking after them. Nothing I can see in the report suggests they should be removed."
But councillor Lynne Sheridan said the elm trees could in fact present a danger but the school should pay to go through a consent process.
"These are trees that literally tip up of the ground. Given the location of the trees in an area that we all know floods, I'd be more worried about these trees tipping over and falling on the school."