About 20,000 Australians on Monday chose to opt out of having an electronic health record created for them.
About 20,000 opted out of Australia's electronic health record system on the first day of a three-month opt-out window despite website glitches.
Almost six million people have signed up for a My Health Record - a digital medical history - over its six years of operations.
But there are fresh concerns of possible cyber-security threats and privacy breaches.
When many people tried to opt out on Monday, the website presented them with errors instead.
"There was a glitch yesterday, I understand, but it's been resolved I've been assured, and about 20,000 people did opt out online yesterday," Prime Minister Malcolm Turnbull told 3AW radio in Melbourne on Tuesday.
The government has opened a three-month opt-out window, ending on October 15, for people who do not want a record created for them.
After this date an e-health record will be created for every Australian by default.
A number of people reported on Monday not being able to log in or get through to a hotline to opt out of the scheme, but the problems were being ironed out.
Health Minister Greg Hunt said world-leading security meant there had been no breaches of the system over the past six years.