ACT Policing detectives arrested the man on Sunday night in the ACT suburb of Parkes and have charged him with arson and damaging Commonwealth property.

Police allege Thursday's fire was deliberately lit. The man is due to face the ACT Magistrates Court on Tuesday.

Three other arrests were made by ACT Policing on Saturday, and the individuals faced court on Sunday.

Two were charged with assaulting a frontline service provider and the third was charged with hindering a territory official.

Ms Andrews said police acted swiftly and wanted to make sure they were doing their job thoroughly.

"I would love there to have been some offenders who were taken into custody much earlier than now," she told 2GB on Monday.

"But I am also confident police have done the work they need to do to make sure the charges against this individual will have the best chance of success when he comes before the court."

The confirmation of the charges came on the same day police arrested a man outside Old Parliament House for trespassing.

Social media footage shows the man being detained by police on Monday.

The 30 minute livestream shows protesters with chains around their hands in what appears to replicate slavery bonds.

The man is seen holding a shovel with burning coals when speaking to an officer, asking to undertake a smoking ceremony outside Old Parliament House.

One officer told the protesters police were happy for a smoking ceremony to proceed but it couldn't be done near the building, which remains closed after the fire.

Home Affairs Minister Karen Andrews said while the right to protest is protected, those who conducted criminal activity will face the full force of the law.

"Every Australian in this country has a right to protest and voice their disagreement with a particular government policy or action; but that does not extend to alleged criminal behaviour," Ms Andrews said.

"They can be anti-anything they like, they just need to protest lawfully."

She branded the protesters' actions as stupidity, saying they had damaged their cause.

"To film yourself and put it up there on social media and be so proud about it as well as being so dumb about it is just extraordinary," she said, referring to Thursday's fire.

"I am really pleased they did because it certainly helped the police, so thank you for that."

Old Parliament House was closed after the front doors of the heritage-listed building were burnt causing potentially irreparable damage.

Police confirmed officials had agreed a small smoking ceremony could take place as part of a peaceful protest but said it got "a little bit out of hand".

Investigations continue into the fire as Australian Federal Police and ACT Policing working to identify other people involved in the fire.

Special Minister of State Ben Morton said the building will be restored and reopen to the public as soon as possible.

Australian Associated Press