A decision on whether to replace a vandalised Captain Cook memorial in inner Melbourne will lie with the local council, says Victorian Premier Jacinta Allan.
The granite Edinburgh Gardens monument was found broken and covered in graffiti over the Australia Day long weekend.
Three days earlier, a statue of James Cook was hacked off at the ankles at St Kilda and another of Queen Victoria near the city's Botanic Gardens was splattered in red paint.
Ms Allan said Yarra Council needed to be a "willing partner" to restore and repair the damaged monument at Edinburgh Gardens.
"The Yarra City Council will need to resolve if it wants to see that reinstated," she told reporters on Tuesday.
"The first and foremost issue is having the City of Yarra make their decision on that."
An email sent to councillors recommended the memorial be permanently removed because it had been vandalised over multiple years in the lead up to Australia Day and was significantly damaged.
The council is yet to decide on its future.
"Council will assess the damage to determine next steps and keep the community informed," a spokesperson said.
They said the memorial had been removed for health and safety reasons, with two witches hats placed at the site on Tuesday morning.
Councillor Stephen Jolly does not want it to be reinstated as he estimates the cost of repairing and replacing the memorial could be several thousand dollars.
"We've got so many other more important things to spend our money on," he told AAP.
Police say their investigation into the vandalism is ongoing.
Port Phillip Council Mayor Heather Cunsolo said there have been preliminary discussions with the state government about offers to assist with the restoration of the Cook statue at St Kilda.
She said council officers and specialists were working to understand the extent of the damage and work out "next steps".
"The statue is secured at council premises while this work is underway," Ms Cunsolo said.
"This means the repair time frame and cost are yet to be determined."
