A public monument of James Cook will be permanently removed from an inner-Melbourne park after a council voted unanimously on the decision.

The monument depicting the colonial figure at Edinburgh Gardens in Fitzroy North had been repeatedly targeted with vandalism, most recently on January 28, 2024.

It has since not returned after being removed by Yarra City Council shortly after for assessment and possible repairs.

The monument's latest vandalism came among a string of damaged Colonial memorials, including a number in Naarm, in the period surrounding January 26 last year.

It was most recently toppled and vandalised with red pray paint reading "Cook the colony" in 2024.

At Tuesday night's council meeting, Yarra City mayor Stephen Jolly boiled the decision down to a "boring economic issue".

Council unanimously voted to support Yarra City officers' recommendations to remove the monument from its collection, with repairs expected to cost $15,000.

In March, Council's Visual Arts Panel made their own unanimous recommendation, noting budget constraints for repair and the monument's poor condition, which was noted as aligning with criteria for removal from collection.

The Visual Arts Panel also noted community contention around the monument, with a 2021 Edinburgh Gardens Conservation Management Plan's assessment of it being 'one of many elements with little or no significance'.

A 2021 'Plaques, Statues, and Monuments in Public Places within Yarra' report also noted Cook is a 'contested figure in relation to First Peoples'.

"I think we have to separate the interesting, fascinating, actually, debate out there in the community about Captain Cook, about whether we should be celebrating these statues of people in the past or not celebrating them," Mayor Jolly said.

"Me, personally, I'm not in favour of demolishing statues of people in the past, even problematic ones."

Mayor Jolly added debate around historical figures in modern contexts is "a slippery path".

The Yarra City mayor said he supported the right for peaceful protests around these types of objects, but that Council was in this case met with a "boring economic issue" of a $15,000 price tag to repair a statue he said was valued at $28,000.

Mr Jolly argued Council couldn't justify those costs to repair an object which would likely be targeted again.

"Don't think if we put it back up it would just be damaged one more time. It would be ongoing, ongoing and ongoing," he said.

A community organisation, the Captain Cook Society, are understood to be interested in taking possession of the plaque.

On Wednesday morning, according to The Age, Victorian Premier Jacinta Allen said it would be disappointing if Yarra City had given in on what she described as efforts for public division among leaders and some politicians.

Mayor Jolly reportedly said the Premier "has systematically bled councils dry of money, but then wants to dictate what councils should spend money on," according to The Age.

Speaking on ABC Radio Melbourne Wednesday, Mr Jolly knocked back suggestions the Council made a 'woke' decision, saying the determination was "about being economically rational".

He added around 20 per cent of road names and statues "left, right and centre" would have to be changed if Council were to theoretically address sentiments to remove references to colonial figures.

"The fact is people were demolishing it, and tagging it….we simply can't afford $15,000 a pop (to repair it)," Mr Jolly said.

"If we wanted to keep it there permanently, we would probably have to have security guards there. We'd probably have to have lighting. That would be tens of thousands of dollars."

Speaking with 3AW Mr Jolly added the monument was only erected at Edinburgh Gardens in 1993.

"I'm not saying this is the perfect solution, but it's probably the best thing we can do right now," he said.