Senior ministers have chastised Christine Holgate after the Australia Post chief spent $12,000 on Cartier watches for senior staff.
Scott Morrison opened the floodgates after declaring the gifts disgraceful and appalling and demanding Ms Holgate step aside.
The prime minister's most senior lieutenants went postal on Friday morning.
"This gifting of expensive watches is completely unacceptable," Trade Minister Simon Birmingham said.
"This type of behaviour is not tolerated, not accepted, and should not occur in the future."
Home Affairs Minister Peter Dutton said people were right to be angry.
"Christine Holgate obviously has come from the private sector and that might be an acceptable way to provide a bonus or reward to staff," Mr Dutton said.
"But in Australia Post where you're talking essentially about taxpayer dollars, the Australian government, the Australian people are the shareholders in Australia Post, then it's unacceptable."
Labor deputy leader Richard Marles said the Australia Post boss was not the only one with questions to answer.
Mr Marles said the chairman made the call on the watches and the board backed his decision.
"This is a board packed full of Liberal mates and there does need to be action in relation to the board," he said.
Australia Post says it will fully cooperate with an investigation into the decision to gift four Cartier watches to senior staff as a reward for a deal to do banking in post offices.
Rodney Boys, the chief financial officer of the government-owned business, will act in the chief executive role during the investigation.
"The Australia Post board and management team will fully cooperate with the recently announced investigation to be conducted by shareholder departments," chairman Lucio Di Bartolomeo said in a statement.
"We remain committed to delivering for our important stakeholders - our people, our post office partners, our customers and the community."
The investigation will be conducted by the federal communications and finance departments, supported by an external law firm, and take four weeks to complete.
Senators spent almost four hours questioning Ms Holgate and her senior colleagues during a Senate estimates hearing on Thursday.
Performance bonuses worth almost $100 million and posties speeding on footpaths because of soaring workload were also scrutinised.
Union leaders slammed Australia Post's leadership over the watches.
CPSU deputy national president Brooke Muscat said members had taken a pay freeze while working harder during the pandemic.
"How are they rewarded? Not with a watch or a bonus I can tell you that," she said.
The estimates hearing was told the total value of incentives was $97.4 million in the 2019/20 financial year.
More than $60 million flowed to 2500 employees involved in the corporate incentive plan, ranging from senior staff to general managers.
A further $21.6 million was "thank you" payments for frontline workers including posties, drivers and processors, while $5.6 million was spent on gift cards for contractors and licensees.
Australia Post's people and culture executive general manager Susan Davies defended the incentive payments.
"I've never seen the amount of volume that's come through. We've worked in extremely difficult circumstances."
Australian Associated Press