Allegations were raised again in the past week about the bank's wholly owned subsidiaries Note Printing Australia and the part-owned Securency, where staff bribed foreign officials to gain contracts.
Labor MP Melissa Parke, chairwoman of the joint Australian Commission for Law Enforcement Integrity committee, said the government should canvass the option of creating a national anti-corruption body for commonwealth agencies.
"The recent revelations concerning the RBA have laid bare the gaping hole in the oversight of the commonwealth public sector," Ms Parke told ABC radio on Saturday.
RBA governor Glenn Stevens told a parliamentary economics committee on Friday that there had been "no cover-up".
In a prepared statement, Mr Stevens defended the central bank's dealings on the issue, saying it had "at all times" dealt appropriately with authorities and responded honestly to questions.
Questions were raised this week about when the RBA first knew of the allegations.
The Accountability Round Table, a non-partisan group including politicians, academics and lawyers, has called for a federal anti-corruption body.
The group's chairman, Tim Smith, a former Victorian Supreme Court judge, said the central bank would have had to send its inquiries to the anti-corruption body.
"Knowing it was there to conduct an investigation and having been a whistleblower, it would have had little option but to refer it to that body," Mr Smith told ABC radio.
Australian Greens leader Christine Milne said there should be a national oversight body similar to those in the states to address corruption in government agencies.
"Whilst we need a national commission against corruption, it does not remove the need for the judicial inquiry into the RBA," Senator Milne said in a statement on Saturday.
I have email Melissa Parke on the low doc con. Her response was that she didn't feel there was systematic problems in the banking section.
Who gives a rats about bribery for a few contracts it goes on everyday. When their are tens of thousands that have been ripped off by fraud by banks and no law enforcements to help.
Apparently Melissa doesn't care about real issues. Just seen Melissa on TV at a anti trawler rally in FREMANTLE concerning the size of the trawler boat.
Yes yes before I get hit with Blogs on save the fish and save the RBA. My family and I would like to be saved from losing our family home after 25 years and $1.5 million of assets that we worked our butt off for.