The ransomware group allegedly behind the hack overnight claimed they had released more sensitive details of customers' medical records on the dark web.
"Added one more file Boozy.csv ...," they wrote in a blog update in the early hours of Friday.
The file, which appears to be related to mental health and alcohol issues, comes after a data dump on Thursday named "abortions.csv".
"You telling that is disgusting (woof-woof), that we publish some data," they wrote on Friday in the blog seen by AAP.
"But we warned you. we always keep our word, if we wouldn't receive a ransom - we should post this data, because nobody will believe us in the future."
The group claimed on Thursday it had demanded a ransom of $US1 for each of Medibank's 9.7 million affected customers, for a total of $US9.7 million (almost $15 million).
Home Affairs Minister Clare O'Neil told parliament the government was standing by Medibank customers, who were entitled to have their information kept private after the "morally reprehensible and criminal" attack.
"I want the scumbags behind this attack to know that the smartest and toughest people in this country are coming after you," she said.
The minister spoke with Medibank chief executive David Koczkar twice on Thursday to "make clear" what was expected of Australia's biggest health insurer and to ensure customers were adequately supported.
"I don't want Australians to have to circulate 14 government departments or areas of Medibank in order to get what they deserve and need," Ms O'Neil said.
"I received the assurance from Medibank ... that if a large data dump occurs, they are fully ready to provide services when and if they are needed to Australians who need them."
The first wave of files dropped on Wednesday included names, birthdates, addresses, email addresses, phone numbers, health claims information, Medicare numbers for Medibank's ahm customers, and passport numbers for international student clients.
Medibank has confirmed details of almost 500,000 health claims have been stolen, along with personal information, after the group hacked into its system last month.
No credit card or banking details were accessed.
Mr Koczkar said the data release was disgraceful and malicious and could discourage people from seeking medical care.
Australian Federal Police investigators are working with international agencies, as well as state and territory police.
Opposition cyber security spokesman James Paterson said anyone who is contacted by a person purporting to have access to their data should immediately report it to authorities.
Senator Paterson has proposed a "safe harbour" provision - involving the nation's cyber security agency, the Australian Signals Directorate, to give companies time in the immediate aftermath of an attack to respond to the crisis without worrying about legal and privacy ramifications.
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