"This is the opportunity for every person over 60 to come forward, no matter what previous hesitation they may have had," he told reporters on Thursday.
Mr Hunt said the AstraZeneca vaccine was an outstanding world-class vaccine that had fuelled first-dose vaccine coverage past 94 per cent over people over 70.
"These vaccines - whether it's AstraZeneca, Pfizer, Moderna - any one of them can save your life and it can save and protect the lives of those around you," he said.
"Please don't wait, please don't hesitate, please come forward."
It is estimated around 300,000 people aged 60 and above were waiting for access to a vaccine other than AstraZeneca.
The latest Therapeutic Goods Administration figures linked nine blood clotting deaths to AstraZeneca from almost 25 million doses in Australia.
The double vaccination rate for Australians aged 16 and over is now 54.2 per cent, while 77.8 per cent have received at least one dose.
The federal government will end business support for states and territories when 80 per cent full-vaccination coverage is reached.
The schemes pumped $13 billion into businesses suffering because of lockdowns, with the figure expected to rise to $20 billion by the time the tap is turned off.
Some restrictions including density limits are expected to continue even when measures are eased at nationally agreed vaccination targets of 70 and 80 per cent.
Highly targeted lockdowns are possible at the higher threshold but states will be expected to foot the bill if restrictions are reimposed.
Treasurer Josh Frydenberg made the announcement about business payments on the same day coronavirus cases in his home state of Victoria soared to a daily record of 1438. There were five deaths.
Despite the spike, he urged Premier Daniel Andrews to move faster on releasing economic clamps similar to the NSW road map.
"Ease those restrictions as soon as it is safe to do so, allow people to get back to work and kids to get back to school," he told reporters.
Support for workers who lose hours because of lockdowns will also be wound down once immunisation goals are reached.
Labor's finance spokeswoman Katy Gallagher said while business payments had to end at some point, some industries needed targeted support.
"Some businesses will not be back to operating at 100 per cent for a fair while yet," she told Sky News.
The NSW government confirmed it would step in to offer support once federal money dried up.
That state reported 941 new cases and six deaths.
Queensland recorded six new local cases on Thursday, with the state government increasing restrictions but resisting a lockdown at this stage.