Prime Minister Scott Morrison is being urged to apologise to former Australia Post chief executive Christine Holgate, who alleges she was "bullied" into leaving her position over the Cartier watches scandal.

There is also growing support for Ms Holgate's call for Australia Post chair Lucio Di Bartolomeo to resign. 

Speaking at the Senate inquiry on Tuesday afternoon, Mr Di Bartolomeo rejected Ms Holgate's claims and said he would not resign.