The Australian Vietnam Forces National Memorial in central Canberra was found defaced with red spray paint on Monday morning.
"Eyes on Rafah!," the message read.
"This is genocide!
"The colony will fall."Â
The daubed phrases were accompanied by an illustration of an eye.
A spokesperson from ACT Policing said law enforcement was aware of recent acts of vandalism.
"Police remind the community that peaceful protest is part of healthy democracy however criminal acts will not be tolerated," they said in a statement to AAP.
Anyone with information has been urged to contact Crime Stoppers.
ACT Policing responded to the graffiti saying criminal acts would not be tolerated. (Mick Tsikas/AAP PHOTOS)
On October 7, Hamas - designated a terrorist group by the Australian government - killed 1200 Israelis and took another 200 hostage during a cross-border assault.
Israel has since unleashed a bombing campaign and ground offensive on the already besieged territory of Gaza that has killed nearly 31,000 Palestinians, displaced 1.7 million Gazans and pushed many to the brink of starvation, according to the United Nations and the local health ministry.
As the violence drags into its fifth month, pro-Palestine protesters have continued marching through the nation's capitals.
Australia has been urged to unfreeze funding to the largest aid agency in Palestine, after suspending its contributions following allegations members of the United Nations Relief and Works Agency for Palestinian Refugees (UNRWA) took part in the October 7 attack.
Politicians across the political spectrum have expressed dismay at the humanitarian crisis and though Australia has yet to change its position, Prime Minister Anthony Albanese said the federal government was taking advice on further support options.
"The consequences of the action that's taken place there should not impact on innocent civilians the way that it has," he told ABC Radio.
"We're giving consideration to the range of support that can be given."
Opposition home affairs spokesman James Paterson acknowledged the gravity of the suffering in Gaza, but said UNRWA should only receive Australian donations if there was a "high degree of confidence" they would not go to Hamas.
"We shouldn't be in any way comfortable with the Australian taxpayers' money potentially finding its way into the hands of Hamas," he said.
Police have urged anyone with information on the vandalism to contact Crime Stoppers. (Mick Tsikas/AAP PHOTOS)
Sweden and Canada have both reinstated funding to UNRWA in recent days, prompting speculation Australia may soon follow.
UNRWA deputy director Scott Anderson said discussions were ongoing with Australian politicians, and outlined steps the organisation has taken since the allegations such as vetting processes and investigations.
The agency has also fired 12 staff.
"It's something we take very seriously," Mr Anderson told ABC Radio.
"It's very unfortunate that the potential betrayal or alleged betrayal by some of the staff will potentially impact the entire organisation, and especially the operation here in Gaza."
The lack of US funding in particular has hurt UNRWA as it is the organisation's biggest donor.
US President Joe Biden has said Israeli Prime Minister Benjamin Netanyahu is hurting his nation by not doing more to avert civilian deaths in Gaza, as a split grows between the leaders.
Mr Biden expressed support for Israel's right to pursue Hamas, but says Mr Netanyahu "must pay more attention to the innocent lives being lost as a consequence of the actions taken".
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