Matthew Scott Hagan was denied bail in the ACT Magistrates Court on Saturday in relation to one count each of arson and possessing a knife and two counts of possessing a prohibited weapon.

Police documents tendered to the court accuse the 32-year-old, who has not pleaded to the charges, of using a blowtorch to set alight a soap dispenser in one of the shopping centre's toilets.

"If the fire was not able to be contained, it could have spread and damaged the building further," the documents state.

The following day after being granted bail, police found Mr Hagan at the shopping centre allegedly possessing knuckle dusters, a serrated knife about 10cm long and a flip knife about 6.5cm long.

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In court, Mr Hagan's mother, Matilda Sanchez, gave evidence about the recent death in the family impacting her son's mental health.

"The death of his cousin has been pretty extreme, overwhelming," Ms Sanchez said.

"He was always a happy-go-lucky guy until he lost his cousin."

The court also heard that Mr Hagan was already on an intensive corrections order when the fresh charges were laid.

Defence lawyer Hugh Jorgensen said the death resulted in his client's health deteriorating.

Special Magistrate Jane Campbell denied bail based on Mr Hagan's criminal history.

Ms Campbell said she did not consider the death in the family as special or exceptional circumstances.

Mr Hagan's matter will be mentioned again in court on July 12.

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