The department is appealing against the man's sentence on the grounds it was manifestly inadequate, and says Chief Justice Terence Higgins did not take into account the harm done to the victims when sentencing.

The man, whose name has been suppressed, admitted having sex with the girl and her 15-year-old friend and using the internet and a mobile phone to groom one of the victims.

In a sentencing hearing in May, the court heard the abuse had continued even after the girl's mother had died and the 35-year-old offender was trying to have himself appointed the victim's legal guardian.

The man was the full-time carer of the girl's mother in 2007 and 2008, and regularly stayed with the woman and her two daughters at their home in Canberra's southern suburbs.

One night in 2007, when the girl was 14, the man persuaded her to have sex with him.

The abuse occurred on several occasions, and two days after the mother had died, the offender had sex with the daughter's 15-year-old friend in the presence of the first victim.

The court heard the offender had discouraged contact between the girl, her sister and their extended family and had allowed her only to call relatives and inform them of her mother's death the day after the woman died.

After relatives became suspicious of the interaction between the victim and offender at the mother's funeral, the girl was removed from his care and sent to live with her cousin in Melbourne.

Police were called when software installed on a computer captured explicit material being sent between the offender and victim.

The man pleaded guilty to grooming a child for sex, an act of indecency in the presence of a child and four counts of sexual intercourse with a person under the age of 16.

Chief Justice Higgins described the crimes as abhorrent, and sentenced him to four years and six months in prison, with a non-parole period of two years and six months.

But the department said he did not give sufficient weight to the objective seriousness of the offences, or to punishing the man.