Dr Nespolon is concerned about the specific parts of the law which he believes "conflict with the aims of delivering good healthcare and improving health outcomes for all Australians".
"Confidentiality and the expectation of privacy is the cornerstone in the provision of healthcare," he said.
Despite receiving some written assurances that police won't be able to access personal health data without a warrant, the Australian Medical Association has asked Mr Hunt to clear up any "perceived ambiguity".
"But it has become clear from a groundswell of both feedback from our members and from the public in general that there is still a perceived ambiguity between the legislation and that potential risk," AMA President Tony Bartone told the Nine Network.
Mr Hunt confirmed he'd spoken with both Dr Nespolon and Dr Bartone about their concerns but wouldn't pre-empt the outcome of a meeting next week.
"I am always open to strengthening those protections to ensure people have complete confidence," he told reporters in Sydney.
Prime Minister Malcolm Turnbull said the government was committed to maintaining privacy of the system.
"If there are refinements or reassurances that need to be given, they will be given," he told reporters in Tasmania.
Mr Hunt stood by his claim police won't be able to access records without a court order, despite the legislation implying they could.
He also insisted it was illegal for insurance companies to access the information.
"Under no circumstances will any element of the record or the record itself be in any shape or form released without a court order."
Deputy Labor leader Tanya Plibersek called on the government to make clear the rules around police accessing online My Health Records.
"When the health minister says the police can't access the record without going to a court but the police say they can, it's a problem," she told ABC radio.
Ms Plibersek is one of six million Australians who already has a digital My Health Record and won't be joining her colleague Ed Husic and Liberal opponent Tim Wilson who have opted out.
The records have been opt-in for the last six years but will become opt-out only from October 15.