Australia’s royal commission into institutional responses to child sexual abuse will be extended by two years at a cost of $126m.

The attorney general, George Brandis, said the government’s decision would alter the commission’s reporting date to 15 December 2017.

“I’m assured by the chairman of the royal commission, Justice [Peter] McClellan, that this will be sufficient to enable the royal commission to complete its work,” Brandis told the Senate on Tuesday.

“The extension of the royal commission will be at a cost of $125.8m. That is in addition to the $377m currently budgeted for, bringing the commonwealth’s total commitment to slightly above $500m.

“Although this is a very significant amount of money, it is the view of the government, given the importance of the royal commission’s work, that this outlay is justified.”

In June, the royal commission’s interim report said a two-year extension was required to allow the inquiry to finish its job.

The report revealed that by the end of 2015 the royal commission would likely have conducted up to 4,000 private sessions and 40 public hearings into institutions which have so far included the Catholic Church, the Salvation Army, Swimming Australia, Scouts NSW, and government-run schools and juvenile detention facilities. The commission needed at least another two years for the extra 3000 private sessions and 30 public hearings it said were necessary, as well as the resulting referrals to police.

“If the royal commission is not extended we will not be able to hold a private session for any person who contacts us after September this year,” the interim report said. “This will deny many survivors the opportunity to share their experiences with us, in particular those from vulnerable or hard-to-reach groups.”

As of July this year there was still a queue of around 1,000 people waiting to tell their story in a private session, as around 40 people called each week. Most survivors who approached the commission had already disclosed the abuse, but it took them on average 22 years to do so, the commission found.

The government said on Tuesday the extension would give the commission “the capacity to hear more stories from victims, conduct more public hearings and issue additional interim reports”.

“Institutions responsible for the care of children will be able to continue to learn from the ongoing work of the inquiry and be better able to prevent child sexual abuse from happening,” said a joint statement issued by Brandis and the social services minister, Kevin Andrews.

“For decades the victims of many heinous offences were silenced, their pain was minimised and the harm to them went unacknowledged,” Brandis told the Senate.

“We now know much more about child sexual abuse than before the commission started its work. We can more easily identify cultural and systemic norms and practices which enabled the perpetuation of these most vile crimes.”

“We know that victims have been harmed not only by the direct experience of abuse but also by institutional indifference and too often rejection of their stories. But there is more to be learned. There is more that needs to be learned.”

The public hearings held so far have detailed incompetence, negligence and, in some cases, alleged cover-ups within institutions when employees were informed of an allegation that a colleague or colleagues were abusing children in their care.

“It is apparent that perpetrators are more likely to offend when an institution lacks the appropriate culture and is not managed with the protection of children as a high priority,” the report found.

“Everyone in a responsible role in an institution must be able to recognise when perpetrators are manipulating or ‘grooming children’. This requires education and training, and the development of an appropriate institutional culture.”

The report also said children were still at risk, and pre-employment checks were inconsistent across the country.

Leonie Sheedy, co-founder of the Care Leavers Australia Network, said the announcement would alleviate a lot of stress for care leavers around the country “who were feeling they would not get the opportunity to have their abuse story heard by the royal commission”.

“It’s a wonderful announcement and we thank the government for the opportunity,” Sheedy told Guardian Australia.

“The real issue is that the churches and charities and state government must contribute to a national independent redress scheme.”

Francis Sullivan, CEO of the truth justice and healing council, which coordinates the Catholic church’s engagement with the commission, said the decision was “absolutely welcome.”

“This is a social investment by our community and a very necessary inquiry,” Sullivan told Guardian Australia.

“It gives people the opportunity to continue to come and tell their story which is one of the big aims of having the royal commission, but also it gives the commission the opportunity to inquire into the institutions who are being named in the private sessions, including the Catholic Church.”

The opposition welcomed the announcement. “Without this extension thousands of stories could have remained unheard, particularly those from vulnerable and hard-to-reach groups,” said a statement from the shadow attorney-general, Mark Dreyfus, and the opposition spokeswoman for women, communities and carers, Claire Moore.

“Labor has been clear that we will support this royal commission receiving all the support and resources required to complete its critically important work.”