Australia is to hold a wide-ranging judicial inquiry into child sex abuse in the country, including investigations into religious organisations, state care facilities, schools, not-for-profit groups and the responses of child services agencies and the police.

The royal commission follows growing pressure for a national inquiry after a senior police officer last week alleged that the Catholic church had covered up evidence involving paedophile priests. However, the inquiry's scope is expected to cover a wide range of institutions involved in the care of children.

"Child abuse, child sex abuse is a vile thing – it's an evil thing done by evil people," said prime minister, Julia Gillard, announcing the royal commission on Monday.

"It's not just the evil of the people who do it. There has been a systemic failure to respond to it. The allegations that have come to light recently about child sexual abuse have been heartbreaking. These are insidious, evil acts to which no child should be subject. There have been too many revelations of adults who have averted their eyes from this evil."

The Australian Catholic Bishops Conference released a statement saying it supported the royal commission and that child abuse was an issue for the entire community, not just the Catholic church. While the statement acknowledged there were significant problems in some Catholic dioceses and religious orders, it rejected suggestions there were systemic problems of sexual abuse in the church.

"It is unacceptable, because it is untrue, to claim that the Catholic church does not have the proper procedures, and to claim that Catholic authorities refuse to co-operate with the police," the statement said.

The most senior figure within the Catholic church in Australia, Cardinal George Pell, also welcomed the royal commission. "Public opinion remains unconvinced that the Catholic church has dealt adequately with sexual abuse. Ongoing and at times one-sided media coverage has deepened this uncertainty," he said.

The conservative opposition leader, Tony Abbott, who once trained to be a Catholic priest, said earlier on Monday he would support a "wide-ranging" commission that did not focus solely on the Catholic church. "Any investigation should not be limited to the examination of any one institution," he said in a statement.

The prime minister's announcement of a judicial inquiry follows allegations last week by a police officer of a cover-up by the Catholic church into child sexual abuse in the Hunter region, north of Sydney.

"I can testify from my own experience that the church covers up, silences victims, hinders police investigations, alerts offenders, destroys evidence and moves priests to protect the good name of the church," he wrote in an open letter to the New South Wales state premier, Barry O'Farrell.

Fox, a veteran of decades of investigations into child sexual abuse, said he had "irrefutable" evidence of a cover-up involving a number of diocese bishops. "It potentially goes even higher than that," he told ABC television.

The following day, the New South Wales state government launched a special commission of inquiry to examine the police investigations of priests in the Hunter region of the Newcastle-Maitland diocese.

In that area, about two hours drive north of Sydney, there are 400 known victims of child sexual abuse. Eleven priests have been charged and convicted since 1995 and six Catholic teachers have been convicted. Three priests are currently on trial.

Last month, police in the state of Victoria accused the Catholic church of intimidation, secrecy, destroying evidence, and failing to report accusations against the clergy in a state-based parliamentary inquiry into sexual abuse.

Deputy Police Commissioner Graham Ashton told the inquiry that the church had also hindered justice by failing to report a single case of child sex abuse in more than 50 years.

"The process is designed to put the reputation of the church first and victims second," he said.

The government aims to consult widely before establishing the exact parameters of the judicial inquiry, which is expected to start in 2013 and take several years to complete.