Greens Senator Lidia Thorpe has posted a tweet appearing to celebrate a fire police say was started by protestors at the Old Parliament House in Canberra on Thursday.

The Victorian Senator made the comments in response to a video shared by ABC News journalist Siobhan Heanue that showed a large fire at the front entrance to the historic building which served as the home of the Australian Parliament from 1927 to 1988.

"Seems like the colonial system is burning down," Senator Thorpe tweeted. "Happy New Year everyone."

The Greens Senator followed up the remark with the hashtag "#AlwayswasAlwayswillBeAboriginalLand".

An hour and over 130 retweets later, the Senator decided to delete the tweet, without offering any apology or clarifying comments.

What's obvious, however, is that if any politician slightly to the right of Stalin were to make a similar remark in response to "right-wing" protests, the media and every political party, including his own, would come down on that politician like a palette of bricks at the corner of the nearest peaceful Antifa or BLM rally.

But that's privilege for you.

According to an ACT Policing spokesperson, there has been ongoing protest activity at the front of the building throughout the past fortnight.

Police said an investigation has been launched into the cause of the fire.