The head of the Australian Medical Association has promised to do “whatever it takes” to ensure My Health Record is subject to the “same level” of protection as existing records in a bid to quell a rising backlash.

The AMA president, Tony Bartone, made the comments on Wednesday at the National Press Club in response to advice from the parliamentary library warning that police can access My Health Record without a warrant.

In a wide-ranging speech, Bartone warned the AMA would campaign on aged care and hospital funding at the next election and predicted the Coalition would match Labor’s pledge of $2.8bn more funding for public hospitals.

Bartone said My Health Record – which will automatically be set up for every Australian unless they opt out by 15 October – had a “very difficult inception” but said patient privacy was the “paramount” consideration for the AMA.

On Wednesday the backlash against the unified patient record gained steam with Labor calling for a suspension pending a review, the Greens and the Australian Human Rights Commission calling for safeguards around warrants in legislation, and Centre Alliance threatening to amend the law.

Bartone revealed the health minister, Greg Hunt, and the Australian Digital Health Agency had given him written undertakings that “without a court order ... there is no way of access to the system for anyone other than the people nominated by the patient”.

The parliamentary library contradicted the health minister by warning that the safeguard was not contained in legislation, leading to the conclusion that the ADHA “cannot routinely require a law enforcement body to get a warrant, and its operating policy can be ignored or changed at any time”.

Bartone said he would meet with Hunt and warned that “any ambiguities” such as a discrepancy in the legislation and practical interpretation “must not be allowed to occur”.

Asked if he would push for the legislation to be amended, Bartone replied he would do “whatever it takes” to put ambiguity “to bed once and for all”.

Bartone was asked if the ability for the ADHA to release My Health Records if it believed it necessary to “protect the public revenue” was of concern. He replied that “the entire section of the legislation ... will be a subject of the conversation” with Hunt.

“It will be important to understand exactly where and where not [disclosure is allowed], and it must be clearly in the public interest, it must be at the same level that exists currently now. That is, a court order or a judicial oversight that warrants us to release those records.”

Bartone stopped short of threatening to withdraw AMA support for My Health Record, saying he was “sure” talks with Hunt could restore settings to “the same level of oversight and care” under which records are currently kept.

Labor’s health spokeswoman, Catherine King, said the ability for law enforcement agencies to access My Health Records without a warrant was “a clear threat to patient privacy and should be changed”.

“The government has made the decision to shift to an opt-out system – it should also tighten the legislation to ensure people’s rights are respected and privacy is protected,” she said.

Labor called on the government to suspend the rollout until a review of the legislation, warning if it did not take “urgent action, the damage could prove irreversible”.

The Australian human rights commissioner, Edward Santow, told Guardian Australia that human rights safeguards “should be in legislation”.

“It would better protect privacy and increase trust in the My Health Record system if the requirement for a warrant for law enforcement to access patient data was included in the legislation,” he said. “Policy can change quickly, without parliamentary oversight.”

The Centre Alliance senator Rex Patrick told Guardian Australia that “on the face of it, there are some unintended consequences from the legislation in its current form”.

“Centre Alliance will write to the health minister urging him to introduce legislation to ensure people’s health data is properly protected,” he said. “On the basis of his public comments, it seems he will be amenable to such a request. If not, Centre Alliance will move an amendment at the first available opportunity.”

The Greens leader, Richard Di Natale, said: “If you want to access someone’s medical records, you should have to have a warrant, simple as that.”

The Australian Conservatives senator Cory Bernardi said he was “open to all suggestions that will enhance individual privacy, the security of data, and to protect people from the intrusion of big government, whether that be from law enforcement or other government departments”.

After byelection campaigns in Braddon and Longman in which Labor has focused on its promised higher health spending, Bartone sounded a note about the AMA’s participation in the next federal campaign.

Bartone said the AMA would be “a very strong and loud advocate” and would “ensure that aged care gets the attention and profile it deserves”.

He welcomed the Turnbull government’s 8.4% increase in recurrent public hospital expenditure between 2014-15 and 2015-16 but said a “one-off modest boost from a very low base is not enough”.

Bartone noted that Labor’s pledge of an extra $2.8bn for hospitals was “significantly better” than current funding.

“I expect that the Coalition will match that as the election draws nearer,” he said. “They do not want another Mediscare-style campaign.”