Political interference was also found to be a factor in the demise of the postal agency's former chief executive Christine Holgate as outlined in a report released on Wednesday afternoon by a Labor and Greens-dominated committee.

Inquiry chair Greens senator Sarah Hanson-Young said Prime Minister Scott Morrison's comments in Parliament sealed Ms Holgate's fate and inconsistent evidence provided by board chair Lucio Di Bartolomeo meant his position was no longer tenable.

"Ms Holgate was denied natural justice, due process, and fair treatment and is owed an apology from Mr Morrison and his government," Senator Hanson-Young said in a statement.

"The purchase of Cartier watches was unwise. However, the treatment of Ms Holgate by the Prime Minister and the Australia Post chairman was disproportionate and denied Ms Holgate of a fair process.

"Throughout this investigation, the committee was concerned with the way the Australia Post board engaged with the inquiry and has serious concerns about the reliability of the evidence given by members of the board, including the chair."

But the Prime Minister's office has hit back at the report's findings, adding it had no intention of issuing an apology to the former boss.

"The government has no intention of responding to a politicised report published by a committee controlled by the Labor and Greens parties," a spokesperson form the Prime Minister's Office told The Canberra Times.

Among the other recommendations the inquiry provided was an overhaul of the board's structure, a review into its incentives and bonuses as well as regular training to staff to better understand the rules.

It also recommended the Australian National Audit Office look at Communications Minister Paul Fletcher's involvement in the standing aside of Ms Holgate along with the agency's governance, including its relationship with government.

Senator Hanson-Young said the inquiry was concerned with evidence provided by the postal agency's board, noting strong ties to the Liberal Party.

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"Given the failings of the board in relation to the Holgate matter, the veracity of evidence given to the committee and the clear issues with protecting the independence and public ownership of Australia Post, the committee has resolved that the chair of the board should resign," she said.

"Australia Post should be independent of government and accountable to the Parliament. It is concerning that the lack of independence of the board and close relationship of members of the board with the Liberal Party means this has not been the case."

A dissenting report by the inquiry's Liberal and National Party senators rejected a number of the recommendations, noting the inquiry had become highly politicised.

It said the audit office would not be able to conduct an audit on ministerial conduct and pushed back on calls to step Mr Di Bartolomeo down from his role as chair, stating he'd worked in a "a constructive manner" during the events.

It also added there was no evidence to support suggestions the postal agency's board had not been acting independently. Previous governments, the dissenting report pointed out, had also appointed directors who had political party ties.

"While the board did have directors who had been associated with the Liberal Party in former careers, previous political involvement does not preclude a post political career for competent individuals from any political party," the response said.

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