Vicki Bates, whose daughter Madison was buried at the cemetery, said it was better knowing that there was just one "mongrel" person involved and police were working hard to find him.
The community had rallied around the families with many turning up yesterday to help clean up the mess, Ms Bates said.
"We had a fireman who came down from Whangaparaoa - he cooked sausages and made drinks for everybody.
"And we had a lady make us a cake for Madison's birthday, because it was her birthday today."
An Auckland Council spokeswoman said the council would welcome any kind gestures by the public "given the terrible loss the victims suffered".
Early childhood teacher Carrie Lagerstedt, from Pukekohe, yesterday offered to "make as many posies as possible" for the children's graves, sparking more than 1000 likes on the Herald Facebook page.
She has been inundated with offers, prompting her to set up a Givealittle page to manage the donations which will go towards buying materials for the posies.
"I've had a really, really great response from the local businesses."
Meanwhile, Mr Rowbottom said the CCTV footage also identified a man who walked through the cemetery about 6.30pm and police believed he might have information that could help the investigation.
About half an hour later a person was seen on CCTV walking through the graveyard and tampering with graves.
He was described by a witness as Maori or Polynesian, about 1.7m tall and of chubby build. He was wearing a green hooded jacket, black baggy pants and work boots.
It was also possible he had a spade with him at some point, Mr Rowbottom said.
"The person responsible for this is likely to have returned home on Saturday evening covered in dirt. Anyone who has suspicions about someone they know who may have been involved in this incident is asked to contact police as soon as possible."
Anyone with information should call Counties Manukau police on (09) 261 1300 or call Crimestoppers, anonymously, on 0800 555 111.
Click here to donate to the flower fund
