"We also want to reassure other families with loved ones buried in the Manukau Memorial Gardens that no other graves were damaged."
Manukau ward councillor Alf Filipaina believed two or three of the graves were "extensively damaged", the others less seriously so.
Filipaina said it was important the families understood the incident was a "pure accident".
"That's one of the key things.
"It's crucial that the families know the graves were not targeted."
The councillor described the incident as an "unfortunate accident".
Council was also putting up signed in the area advising people of the incident and asking visitors to pass this on to the affected families.