The Federal Opposition believes it has enough support to establish a Senate inquiry into abuse at the Nauru offshore detention centre, following the leaking of thousands of incident reports from the centre this week.

The documents were leaked to The Guardian, a number of which detail allegations of abuse at the centre — some involving children.

During the week, Immigration Minister Peter Dutton stressed a significant proportion of the claims would relate to minor matters such as complaints over the centres food and children not going to school.

However, he said serious claims of abuse would be properly investigated by Nauruan authorities.

Opposition Leader Bill Shorten said that response was not good enough.

"What we see in Nauru requires the attention of the Parliament," Mr Shorten said.

"I support regional processing, but I don't believe you should have regional processing at the price of indefinite detention.

"The Federal Government needs to stop brushing these matters under the carpet. If there's nothing wrong happening here, then they shouldn't worry about scrutiny."

Manager of Opposition Business in the Senate Sam Dastyari said the inquiry would find "what it will find" when questioned as to whether the decisions by the former Labor government could be under scrutiny.

But he insisted the focus would be on the Coalition.

"At the heart of this is this secrecy fetish that's been run by this Government, and this idea that says that we can cover this up and hide it," Senator Dastyari told ABC's Insiders.

"The bit that I just can't comprehend is why the simple idea that was presented by Bill Shorten this year, having an independent child advocate, wasn't leapt upon by the Government.

"If there's nothing to hide, why can't we go to Nauru now? Why can't you jump on a plane this afternoon and try to find out what on earth is going on there?"

When asked if he would get the support Labor needed for an inquiry he said: "I believe so."

The Opposition, along with the support of the Greens, would likely have to convince another four senators to back the calls for an inquiry.

Earlier, three non-government organisations called for the royal commission into child sex abuse to widen its inquiry to include alleged abuse of asylum seekers on Nauru.