Australian Federal Police will investigate whether independent senator Lidia Thorpe broke laws by saying she is prepared to "burn down Parliament House" in support of Palestinians.

Senator Thorpe said her remarks at a pro-Palestine rally were "clearly" a figure of speech.

But in a rare public statement, the AFP confirmed it would consider whether the comments breached legislation.

"This will be done methodically," an AFP spokesperson said.

"It is not the usual practice of the AFP to provide a running commentary on matters.

"However, noting the public commentary and concern, the AFP is seeking to reassure the community that this issue is being appropriately considered and undertaken in a timely manner."

At a rally in Melbourne on Sunday, the firebrand senator for Victoria compared the

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