Greens leader Adam Bandt doesn't rebuke Jordon Steele-John over free speech comments related to vandalism of Australian War Memorial

Pro-Palestine graffiti on the Vietnam War Memorial on Anzac Parade in Canberra.  (Supplied)

Australian Greens leader Adam Bandt has refused to answer whether vandalising the Australian War Memorial is a legitimate form of protest.

The Australian National Korean War Memorial, Australian Vietnam Forces National Memorial, and the Australian Army National Memorial were graffitied with pro-Palestine messages on Saturday night.

On Monday Greens senator Jordon Steele-John refused to support a motion from Tasmanian senator Jacqui Lambie to condemn those who desecrated the memorials.

Senator Steele-John said the Greens would not support Senator Lambie's motion, saying war memorials were "not politically neutral spaces".

"The Australian Constitution contains no explicit commitment to freedom of speech," he said.

"If we are to believe that the men and women of the ADF gave their lives in wars and conflicts to defend such freedoms, then you have to engage with the reality that protesting, that painting is a form of speech."

Asked by 7.30 host Sarah Ferguson if Mr Bandt agreed with Senator Steele-John that it was a form of free speech, the Greens leader refused to answer the question.

"We might have differences of opinion about whether or not Australia should be going to war, but we always respect people who are sent to war," Mr Bandt told 7.30.

"And we've also made it clear that when it comes to making people's voices heard, we want to see peaceful protests."

Pressed on the issue of whether he agreed with Senator Steele-John's comments, Mr Bandt criticised Prime Minister Anthony Albanese and Opposition Leader Peter Dutton instead.

"The prime minister, and the leader of the opposition today, were more agitated about graffiti than they have been about the slaughter of people in Gaza," Mr Bandt said.

"A genocide is taking place.

"We have an extremist government [in Israel] that is subject to orders to stop genocide — and the thing that the prime minister and the leader of the opposition seem to get most agitated about is graffiti today.

"Children are dying."

Leaders united in condemnation

Earlier Mr Albanese said that the desecration of the monuments was criminal.

"I do not know what goes through someone's head in thinking that a cause, any cause, is advanced by the desecration of what are sacred sites here in Australia," the PM said during Question Time.

"I hope sincerely that these people who are responsible are found, they get the full force of the law, and they get the book thrown at them."

It was a sentiment echoed by Mr Dutton.

"I hope that the police can double down on their efforts to identify these people [and] allow a very clear message to be sent to those of a similar mind that these acts are not to be condoned in our society," he said.

Mr Bandt had previously criticised violent attacks on MPs offices and said he wanted protest to be peaceful but said he would not be lectured to by the leaders of the two main parties in Australian politics.

"I want to see peaceful protest ... and I want to see peace in Gaza," he said.

"I am not going to be lectured to by a prime minister and a leader of the opposition, who back the invasion of Gaza and refuse to use the levers at their disposal to put pressure on an extremist government to stop a genocide."

Mr Bandt stopped short of saying whether the Greens would put forward another motion to the Senate for the Australian government to recognise the state of Palestine.

He also said he had not approached exiled Labor senator Fatima Payman about joining the Greens.

Senator Payman was suspended from the Labor caucus at the weekend after she said she would again cross the floor if faced with another Senate motion to recognise the state of Palestine.

He did however chastise Labor for its treatment of her.

"We want the government to shift its position," he said.

"There's been multiple opportunities for Labor to put some pressure on Benjamin Netanyahu, it is just wrong that Labor is putting more pressure on Senator Payman than on Benjamin Netanyahu."

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