The Labour leadership contender was asked about the investigation into ex-prime minister Sir Edward Heath and other police probes during the West Belfast Talks Back debate at Féile an Phobail (West Belfast Festival).
"There has to be a standing commission to investigate this, the trauma that victims of childhood sexual abuse go through and carry it with them for the rest of their lives.
"If there were cover-ups because the alleged perpetrator was a very prominent person at that time the law should apply to everyone, whoever they are, absolutely equally.
"We should be very careful that just calling someone an abuser is not the same thing as proven evidence, the proven evidence has to be before any final decision is made."
Earlier Mr Corbyn said the British Government needs to fund Northern Ireland's welfare system properly and warned of increased poverty because of Tory plans.
The devolved powersharing administration in Belfast is at an impasse over measures to cut the cost of benefits, which the Government says are necessary to reduce the deficit and encourage work but Sinn Fein believes will hurt the most vulnerable.
He told BBC Radio Ulster's Nolan Show: "The British Government is the one that should step up to the plate on this because what they are essentially doing is not providing either the resources to the Assembly to fund the welfare system properly or allowing the Assembly to do it itself with the money, so we need a change by the British Government more than anything else."
Mr Corbyn has burnished his credentials with the Left by defying acting leader Harriet Harman to vote against the Government's Welfare Bill.
The other leadership candidates fell into line by backing the Opposition's "reasoned amendment" to the legislation - which was defeated - and then abstaining on whether it should progress to the next Commons stage.
He said: "It seems to me that we should not be allowing the welfare reform Bill to go through in the British Parliament.
"Essentially this is a budget issue at the present time and the British Government should be funding Northern Ireland properly."
He said there would be increased poverty because of the welfare plans.
The Government has not said Northern Ireland's ministerial Executive cannot fund an enhanced welfare system but has maintained it is not prepared to pay for more expensive arrangements than in the rest of the UK.
A Northern Ireland Office (NIO) spokesperson said: "The SHA is a good deal for the people of Northern Ireland and represents the best hope for a brighter, more secure future. It needs to be implemented in full, including welfare reform.
"Without welfare reform the Executive's finances are increasingly unsustainable, hitting public services and undermining the credibility of the devolved institutions.
"The UK Government cannot fund a more generous welfare system in Northern Ireland than in the rest of the UK.
"But the top-ups agreed by the five Executive parties in December would give Northern Ireland the most generous system of anywhere in the UK. All parties need now need to fulfil the commitments they made."