The Ministry for Culture and Heritage memorials and taonga manager Brodie Stubbs said it was unknown whether the attacks were connected.
He said no one had been held accountable for the vandalism so far.
"We've had some reports about people with dogs but we haven't actually got any direct evidence of that."
He said there's been no more attacks at the war memorial since security patrols were increase.
Lambton Ward city councillor Nicola Young was shocked at the "appalling and mindless" vandalism.
"It's particularly shocking because it is a war memorial park and I feel that they're really vandalising the legacy and memory of the people who died in the wars for us."
Young said nature was not just about making the city look pretty.
"It's also about keeping us healthy. These trees are acting as lungs for the city and they also make it look beautiful too.
"But it's very easy in cities to become disconnected from nature, so that makes trees and gardens particularly important."
She said the people responsible were "idiots".
"These people are fools and they're destroying things that make the city beautiful and they destroy it for everybody."
The attacks follow a recent fruit heist at the Memorial Park where apples were stripped from trees outside the education centre in the dead of night.
