The Australian Federal Police has issued a rare statement confirming it is investigating whether independent senator Lidia Thorpe broke any laws by saying she was prepared to “burn down Parliament House” in support of Palestinians.

In a widely condemned speech over the weekend, Senator Thorpe declared she would “burn down Parliament House to make a point” as she compared the struggle of Palestinian people in Gaza to that of Indigenous Australians.

A police spokesperson told the ABC the AFP had called upon its newly established National Security Investigations (NSI) team in Victoria to investigate whether the comments “breach legislation”.

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“This will be done methodically. 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,” the spokesperson said.

In a separate statement, Senator Thorpe said her remarks were “clearly a figure of speech” and did not amount to “a literal threat”.

The NSI teams, set up under new commissioner Krissy Barrett, deal with the blurring lines between extremism, political violence, organised crime and foreign interference, investigating behaviours and offences that do not meet the strictly defined threshold of terrorism.

The opposition said it would “consider options” to hold Senator Thorpe to account.

“Lidia Thorpe’s comments are disgraceful and shocking, but unfortunately unsurprising,” Senate Opposition Leader and Shadow Foreign Affairs Minister, Michaelia Cash told the ABC.

“Australians deserve much better from their elected representatives, but she has a long history of appalling conduct. The opposition will consider options available within the Senate to hold Senator Thorpe accountable and ensure the safety of all those who work in our parliament.”

Home Affairs Minister Tony Burke told ABC RN Senator Thorpe’s comment was unacceptable and that if the temperature could be lowered in Gaza, “it should be able to be lowered in Canberra.”

“The concept of wanting to inflame, push the temperature up, is not what anyone should be doing, least of all a member of parliament,” he said.

Mr Burke, who manages government business in the House of Representatives, did not indicate whether the government would pursue any action against Senator Thorpe in the Upper House.

Social Services Minister Tanya Plibersek also criticised Senator Thorpe’s remarks, calling them “absolutely irresponsible”.

“We just don’t want to give it extra air,” Ms Plibersek told Seven’s Sunrise.

“We’re holding our breaths. We want to see the hostages returned tonight as they’re supposed to be.

“We want to see aid back into Gaza and the rebuilding of Gaza, we want to see peace in the Middle East.

“We don’t want conflict brought here to Australia.”