Prime Minister Scott Morrison told Sydney's 2GB radio that he stands by his statement made in Parliament earlier this week that Australia Post chief executive Christine Holgate "can go" if she did not wish to stand aside but noted that it was a matter for its board.
"But the direct engagement between the board and Ms Holgate is for the board," he said.
He was also reticent to reveal who told Holgate to stand down.
"I'll leave that to the Australia Post board to respond to," Morrison said when asked.
Holgate's lawyer Bryan Belling claims there are no legal grounds for her to stand down. He also accused Morrison of humiliating Holgate when Morrison said in Parliament that giving the Cartier watches to executives was an appalling abuse of taxpayer's money.
Morrison's comments came after a Senate estimates hearing where the purchase of the watches was revealed during questions from Labor senator Kimberley Kitching.
Australia Post is being investigated over its gift and expense culture after the Post spent almost $20,000 (US$14,000) on watches for senior executives as bonuses in 2018 after reportedly increasing the Post's bottom line by $75 million.
Morrison said the terms of reference for the inquiry into Australia Post is broader than just the matter of the Cartier watches.
The chairman of Australia Post, Lucio Di Bartolomeo, says the decision for Holgate to step aside was mutually agreed on Oct. 22, while the one-month investigation takes place. However, Holgate's lawyers say she has not formally been asked to step down.
Business leaders have defended Holgate and argue she has been grossly mistreated.
Home Affairs Minister Peter Dutton said Holgate was a very decent person who made a mistake in relation to the Cartier watches.
"It's a perfectly acceptable act if you're in a publicly-listed company or a private company," he told the Nine Network.
"But when you're dealing with taxpayers' money as part of the Australia Post network it's a different standard and different expectations."
Deputy Opposition Leader Richard Marles said the luxury watch scandal was completely unacceptable, particularly given service and mail delivery times were going backwards at Australia Post.
"I think Christine Holgate and Australia Post have a lot to answer for," Marles said.
An Australia Post spokesman told AAP it had communicated frequently with Holgate and ensured she received support.