Labor tried to pass a 12-month extension, but the crossbench would only agree to a shorter delay before millions of Australians are automatically signed up for a digital health profile.
The deadline for Australians to opt out of My Health Record has been extended until the end of January after the Senate voted in favour of a delay.
The extension was confirmed by health minister Greg Hunt on Wednesday afternoon, amid reports the opt-out website was crashing under the weight of last-minute applications.
The opt-out window was due to close on Thursday and the majority of Australians would have had an online health record created in their name to allow the easy transfer of records between authorised doctors and specialists.
Labor attempted to rush through amendments in the Senate that would force the government to delay the end of the opt-out period by 12 months, but the crossbench powerbrokers would only agree to a more modest extension of less than three months.
Coalition senators did not oppose the extension, and health minister Greg Hunt confirmed on Twitter the Digital Health Agency would not proceed with automatic enrollments until January 31 next year.
Mr Hunt said the government had "worked with" the Senate crossbench to extend the deadline.
About 4 per cent of Australians (1.147 million) have so far opted out of the electronic health record system, while around 300,000 have opted-in and created a digital record in the same period.
Many users took to social media on Wednesday, complaining of jammed phone lines and a glitchy website that were making it impossible to opt out before the deadline.
The government has already agreed to a suite of privacy reforms but is yet to bring them to a vote in the Senate.
The changes, supported by both sides, will close a loophole that might have given domestic abusers a way to track fleeing relatives by accessing their children’s digital health profiles.
There will also be tougher penalties, up to five years in jail, for “misusing” the data.
In earlier changes, the government agreed to clarify the wording of the law to make sure police and other agencies could only access the record with a court-ordered warrant.
The Senate had already passed a motion urging the government to delay the opt-out, so further privacy improvements could be made and Australians could have more time to make up their minds.
Almost the entire crossbench - including the Centre Alliance and One Nation blocs - voted for the motion that "called on" the government to act.
Labor has promised to task the Privacy Commissioner with a review of the legislation if it wins the next election, to check for any further weaknesses in the system.
Opposition health spokeswoman Catherine King said My Health Record promised huge benefits for people which participated, but they had been jeopardised by the Liberals shifting away from Labor's opt-in model.
"Their botched rollout has seriously undermined public trust in this important reform and it's going to take time to rebuild it," Ms King said in a statement.
Ms King said the original opt-out period would have ended before the government could pass privacy protections it had already agreed were needed.
"The My Health Record opt-out period must not end until the clean-up legislation has passed the parliament."
She said the 12-month extension would give the government time to reach Australians with a new public information campaign.
Health Minister Greg Hunt argues there have been no cases of misuse of information in the six years the system has operated, but the government was willing to provide further protections.
It is not clear when the government plans to push its privacy amendments through the parliament.