The Australian Heritage Council has determined existing laws provide "adequate" protection for sites and monuments that relate to Australia's colonial history.
Federal Environment Minister Josh Frydenberg asked the Council to look into whether additional protections were needed after a Captain Cook statue in Sydney's Hyde Park was vandalised last year.
The report, which was provided to the Minister in March, has just been released.
The Council assessed the legislative protections available at local, state and federal levels, and the penalties available under existing legislation.
It found that vandalism of statues is covered as an offence under property damage, even when the particular monument has not been awarded heritage listing.
The Council made mention of the vandalism of the Captain Cook statues and other monuments in its report.
"In Australia in September 2017, following demonstrations in relation to confederate statues in the US, a number of colonial monuments in Australia were vandalised. In Sydney’s Hyde Park a statue of Captain James Cook was sprayed with slogans.
"Monuments to Queen Victoria and Governor Lachlan Macquarie were also targeted. In Perth, the statue to Yagan, an Indigenous resistance warrior has been repeatedly targeted over a number of years, by beheading."
Other recommendations were that Indigenous stories of colonisation be told alongside those of British arrival at key sites, and - due to the changing nature of social attitudes - there should be a national conversation about how Australia's colonialist history is memorialised.
"Respect and awareness of Indigenous issues and treatment in Australia, not just in colonial times, is vital in countering the types of political protest which result in vandalism to colonial statues as has been recently seen."
The report also highlighted how the adding explanatory plaques has been successfully done, such as with the Explorers' Monument in Fremantle.
It also recommended a consideration of "how statutory protections for Indigenous heritage places more broadly can be made more effective".
In a statement to NITV News, Minister Frydenberg said he believed the $50 million redevelopment of Botany Bay - which includes $3 million for a Captain Cook monument - is in keeping with this "shared history" approach.
“Now through the Kamay 250th Anniversary Project we will be able to recognise the first contact between Indigenous Australians and the British and our shared history,” Minister Frydenberg said.
“As the Australian Heritage Council makes clear, such recognition of our shared history is important as it helps to build community support and engagement with our places and monuments.”