During a debate over the protests in the Senate on Wednesday, Senator Hanson labelled George Floyd - the man whose brutal death at the hands of Minneapolis police sparked a global movement - a "criminal and a dangerous thug".

"It sickens me to see people holding up signs saying Black Lives Matter in memory of this American criminal," Senator Hanson said.

"No one could possibly condone the way in which George Floyd died but what upsets me is the attitude of many people, black and white that his death matters more because he is black.

"More whites die in Australia and America in relation to deaths in custody than blacks. That's a fact. But where is the outrage for white people?

"When a white 40-year-old Australian-American woman by the name of Justine Damond was shot there was no protest, no one really cared because she was white."

In fact, hundreds of people attended a vigil for Ms Damond, who was shot in 2017.

The conviction of former US police officer Mohamed Noor last June over Ms Damond's death was the first ever murder conviction against an on-duty Minnesota police officer - the same police force responsible for Mr Floyd's death.

Senator Hanson also labelled calls to reduce Indigenous incarceration rates as "brainless".

"Black and white Australians must face punishment if they commit an offence or break the law," Senator Hanson said.

"We cannot allow bleeding hearts and those on the left to destroy the fabric of our society and our freedom."

Greens senator Janet Rice, who is facing calls to be tested for coronavirus after attending a Black Lives Matter protest on the weekend, said the "racism expressed" by Senator Hanson was part of the reason people had mobilised.

"None of us would choose to protest during a pandemic, but we do not have a choice when black lives are being lost and our government refuses to do anything about it," Senator Rice said.

"The true matter of public importance we should we debating here today is the deaths of 437 First Nations peoples in custody in almost three decades since the royal commission into deaths in custody."

Greens senator Mehreen Faruqi, who also attended the protests, said "racism is killing people and I won't stand by".

"Stop trying to divert attention from the real issue of deaths in custody," Senator Faruqi said.

"You stand here and shame the protesters. Shame on you. Where is the rage?"