Covid-19 daily infections in Sydney have fallen for a third straight day but still linger near record levels as the outbreak spurs a spike in vaccination rates in the hard-hit western suburbs of Australia's largest city, Reuters reports.

Officials have promised residents in Sydney, the epicentre of Australia's worst coronavirus flare-up, more freedom once vaccinations reach first 70 per cent, then 80pc, as a lockdown now into its eleventh week fails to quash the Delta variant.

"Don't be left behind when we start opening up. When we open up at 70pc double dose, it will be only for those who are vaccinated," New South Wales state Premier Gladys Berejiklian said at a media briefing in Sydney, the state capital.