Senator Lidia Thorpe is being investigated by Australian Federal Police after saying she's prepared to "burn down Parliament House" in support of Palestinians.
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."
Lidia Thorpe said that she had always rejected violence and was committed to pursuing justice through peaceful, democratic means. Source: AAP / Mick Tsikas
"So we stand with you every day, and we will fight every day and we will turn up every day and if I have to, burn down Parliament House to make a point," she said, to cheers from the crowd.
The comments sparked a political firestorm, with Home Affairs Minister Tony Burke urging leaders to avoid inflaming community tensions.
He said the natural instinct when "offensive" comments were made was to "increase the pressure."
"I don't think that's in the interests of social cohesion," he told reporters in Canberra.
He said her comments "speak for themselves ... but I also don't think us raising the temperature in return does anything other than create a problem".
Thorpe clarified her comments on Monday, saying they were "a metaphor for the pain in our communities".
"They were obviously not a literal threat," she said in a statement.
"This mock outrage is ridiculous. While people are dying and starving in Gaza, politicians and media are once again clutching their pearls and chasing a scandal."
Deputy Liberal leader Ted O'Brien said the comments went against Australian values.
"To be making those sort of statements are absolutely appalling ... and to hear the roar of the crowd, that's deeply concerning," he said.
Both sides of politics are hoping the release of Israeli hostages and the next stages of the ceasefire deal in Gaza will help soothe community tensions at home.
