The incident was raised at an ACT government estimates committee hearing by Greens MLA Caroline Le Couteur on Thursday morning.

The two trees were cut down during works in Wanniassa in 2017 despite being heritage listed.

One tree was accidentally cut down by an ACT government contractor, then mulched before the incident was "self-reported" to the ACT Heritage Council, the estimates committee heard.

"How do they realise to self report it and simultaneously mulch it? It doesn't make sense," Ms Le Couteur said.

According to ACT heritage director Fiona Moore, it was unknown how the second scarred tree was cut down or who did it, but it was reported by a member of the community six months after it was felled.

ACT Parks and Conservation was able to secure this trunk and is storing it in a secure area.

Ngunnawal elder Wally Bell said the loss of the trees represented a loss of 25,000 years of Indigenous culture.

"Every part of the landscape has a different story to tell and by removing those things from the landscape, we're taking away those cultural stories," Mr Bell said.

"There's a lot of that total disregard."

The trees were scarred by Indigenous people, who used the bark to form shields, canoes or other objects, Mr Bell said.

"We've occupied this area for 25,000 years and in that time everything that we needed comes from the natural environment," Mr Bell said.

But despite the loss, Ms Moore told the estimates committee there was little action the government could take to punish those responsible.

"These two incidences actually highlighted that there needed to be more enforcement provision within the heritage act," Mr Moore said.

"At present the range of options are very black and white ... either education or prosecution."

But prosecution meant a lengthy process through the courts to issue fines.

Environment and planning directorate chief operating officer Craig Simmons told the estimates committee there was an onus of proof to prove intent to damage.

"That is a very difficult intent to prove," Mr Simmons said.

"The element of intent with respect to heritage has been a difficult hurdle to get over."

"There is a strict liability offence in the [heritage act] but it's not replicated in the Magistrate's Court."

Planning minister Mick Gentleman told the committee he has asked the directorate to review what the government could do to strengthen the act.

"Once that work is done we'll be able to then look at those opportunities for enforcement," Mr Gentleman said.

Speaking to The Canberra Times, environment directorate executive director Ian Walker said this could mean on-the-spot fines and repair orders where appropriate.

While Mr Walker said the investigations had been concluded, Ms Moore told the committee the council hoped to have the matters completely resolved by the end of the year.

Ms Moore told the committee there was little else she could say on the matters due to privacy reasons.

Speaking to The Canberra Times, Ms Le Couteur said it was likely the committee would recommend stronger enforcement powers.

Elder Mr Bell said the laws needed to change.

"Everybody knows who's responsible for those sorts of damages ... but nobody seems to be getting any form of reprimand," he said.

"I think the legislation needs to be revised and incorporate some sort of mindset to hurt them in the pocket."