It comes as the establishment of a Commonwealth anti-corruption watchdog ahead of the next federal election is becoming increasingly unlikely with opposition and crossbenchers criticising the federal government's "weak" proposal.

An overwhelming majority of public servants who believed they had witnessed corruption within the Attorney-General's Department and the Department of the Prime Minister and Cabinet did not report it, data in the bureaucracy's latest census has revealed.

While the levels of public servants across the two departments witnessing suspected corruption remained low at less than 5 per cent, few felt the need to report it.

Only 5 per cent of staff in the legal policy department, who has been leading the charge on developing the government's integrity proposal, said they reported the potential corruption - 14 per cent lower than the public sector's overall figure.

But 84 per cent said they did not report the possible misconduct.

In the Prime Minister and Cabinet's Department, the hesitance to report rose slightly further to 85 per cent with less than 10 per cent reporting the behaviour in accordance with the agency's policies and procedures.

Allegations of cronyism and nepotism rated among the highest types of corrupt behaviour across the two departments while acting, or failing to act, on possible conflicts of interest reached a third in the Prime Minister's department.

Almost one in five staff members who said they'd seen corruption across the two departments reported it was "green-lighting" - where a bureaucrat unfairly favours or disadvantages specific parties in a decision-making process.

A PM&C spokesperson said public servants had a responsibility under the APS code of conduct to report potential misconduct.

"PM&C takes a zero tolerance approach to fraud and corruption and have strong processes and internal controls in place to prevent it," a spokesperson said.

"Since the census survey, the department has undertaken steps to strengthen staff training in fraud awareness and reinforce that it is everyone's responsibility to report it under the APS Code of Conduct."

Regular fraud training was also conducted at the Attorney-General's Department, a spokesperson said.

It also had systems in place to ensure staff who stepped forward to report corruption were not "adversely disadvantaged, discriminated against or victimised as a result".

The public service commission's State of the Service report revealed earlier this week that public servants believed reporting alleged unwanted behaviour could affect their career or upset relationships in the workplace.

But more than half said they didn't report possible misconduct because they believed no action would be taken.

On the other hand, the Home Affairs and Defence departments recorded the highest levels of corruption reporting across the 14 agencies.

Labor's public service spokesperson Senator Katy Gallagher said the figures were "deeply concerning" as the opposition and crossbenchers pushed for stronger measures to be included in the federal government's proposed integrity body during the year's last sitting week.

Under the model put forward by the government, the integrity commission could only investigate suspected criminal misconduct and could only be referred to them for investigation by a minister or department head.

The ACT senator said Mr Morrison needed to set an example from the top.

"It's deeply concerning to see that the Prime Minister's own department and other senior departments are recording extraordinarily high levels of non-reporting of suspected corrupt behaviour," Senator Gallagher said.

"Trust in the public service and its own integrity processes is fundamental to a well-functioning democracy. If public servants don't report suspected corrupt behaviour or don't feel able to, it weakens and erodes public trust in our institutions.

"These concerning statistics should also been seen in the context of the Prime Minister and his government refusing to introduce legislation for a national anti-corruption commission. Leadership matters here, and we don't have any coming from the government."

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The agency-level data of the public service's 2021 census, which was released on Tuesday, also showed the relatively low reporting levels of harassment and bullying within departments.

The overall rate across the APS for reporting the behaviour remained relatively low at 33 per cent but the Attorney-General's and Foreign Affairs and Trade departments recorded just 24 and 25 per cent respectively.

Sexual harassment complaints in the public service more than doubled in the year to 78, with the central agency agreeing more needed to be done to fix the culture.

The number of general bullying and harassment complaints made by federal public servants also jumped from 422 two years earlier to 588 in 2020-21.

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