Australia announced its first coronavirus-related death in the current Sydney virus outbreak on Sunday, as the country's biggest city struggles to bring the Delta variant under control.

The woman in her 90s died Saturday, hours after testing positive for Covid-19, and was also the first death from a locally-acquired infection in Australia this year.

It came as authorities announced a record 77 new cases, and warned that numbers were expected to spike above 100 on Monday.

"Tomorrow and the few days afterwards will be worse, much worse than we've seen today," New South Wales state premier Gladys Berejiklian said.

Sydney is now in its third week of lockdown, but the number of new cases continues to grow among a population that is overwhelmingly unvaccinated.

Lockdown rules were tightened Friday and Berejiklian warned that stay-at-home orders were expected to remain in place unless there was a dramatic turnaround.

"Given where we're at and given the lockdown was supposed to be lifted on Friday, everybody can tell it's highly unlikely at this stage, given where the numbers are," she said.

Sydney has recorded 566 new infections since the beginning of the outbreak mid-June.

While that is low compared to most global cities, Australia has taken a zero-tolerance approach to widespread community transmission throughout the pandemic.

Authorities have been quick to impose restrictions in an attempt to stamp out clusters early, and the country's borders remain largely shut with only about 10 percent of Australians fully vaccinated.

The government launched a new advertising campaign Sunday encouraging people to "arm yourself" against Covid-19 by getting jabbed, though vaccines are yet to be offered to most under-40s.

Chief Medical Officer Paul Kelly said other "graphic" adverts would be broadcast in Sydney urging people to follow stay-at-home orders, as police step up enforcement amid reports that flouting of the rules was widespread.

Australia has recorded just over 31,000 cases of Covid-19 and 911 deaths in a population of about 25 million to date.