Two leading MPs have faulted the Reserve Bank of Australia (RBA) for mishandling the bribery scandal that involved officials of Note Printing Australia (NPA) and Securency, which are under the direct supervision of the central bank.

In his appended comments to the parliamentary economics committee report tabled on Thursday, Australian Greens MP Adam Bandt said the RBA acted irresponsibly in not calling the attention of the Australian Federal Police (AFP) when it became clear that NPA and Securency officials were engaged in bribery of foreign nationals to win lucrative banknote printing contracts.

Both RBA governor Glenn Stevens and his former deputy, Ric Battellino, were sounded off on the scandal in 2007 but instead of alerting the police the bank chose to hire private law firm Freehills to probe on the matter, the report said.

Mr Bandt scored Mt Steven's defence that the Freehills investigation led to conclusion that no Australian laws were violated and no compelling reasons were seen to get the AFP involve in the matter though the law firm had raised concern on the manner NPA officials had conducted their business dealings with foreign officials.

"The (Freehills) report wasn't positive evidence of the absence of wrongdoing, but rather a statement that no conclusive findings of illegality could be made," the Greens MP was quoted by Fairfax as saying in his comments to the committee report.

He noted that eventually Mr Stevens would concede that the RBA should have relied on the AFP to step in to begin with, which was a belated realisation that only left as cloud of doubt "over the Reserve Bank and its governance until a full inquiry is conducted."

The committee report also determined that the testimonies given by RBA officials during the October hearings were insufficient, leaving only more questions begging for solid answers.

"Most significantly, there is still no satisfactory explanation as to why the police weren't called when the RBA was first presented with credible allegations of illegality, possible corruption and impropriety," Mr Bandt was reported by the Australian Associated Press (AAP) as saying.

To remedy this, Mr Bandt has called for a full-blown inquiry that would establish the real facts behind the case and would accommodate suggestions to correct the previous missteps of the RBA and to strengthen its corporate governance.

For his part, Liberal MP Tony Smith dismissed claims by the RBA that the manner it handled the case was best explained by its intent to protect the whistleblower that brought the scandal into light.

The explanations offered by Mr Stevens and Mt Battellino were best described as "threadbare ... and less than persuasive."

"The narrative presented to date by the governor and his former deputy lacks precision and clarity. And this has had the unfortunate effect of making the bank appear reticent and even secretive," Mr Smith was reported by Fairfax as saying.

The incident and the way top RBA officials have behaved only supported earlier calls that the central bank be subjected into direct oversight of the Parliament, Mr Smith said, adding that RBA officials should appear more frequently each year before the House of Representatives.

In a statement, the RBA said all necessary measures to fully address the issue was not spared and top officials of the bank cooperated with the full course of the investigation.

"We have sought at all times to deal appropriately with all the issues that have arisen, and to cooperate with the legal authorities. We have also sought to respond honestly to questions from this Committee," The National Times quoted the RBA statement as saying.