CANBERRA, July 30 (BBC) - Australia's virus-hit state of Victoria has reported its worst death toll and case rise - prompting fears that a lockdown of state capital Melbourne is not working.

The second-most populous state confirmed 13 new deaths and 723 new cases on Thursday - a 36% jump on the previous daily record set on Monday.

The spike meant Australia overalls had its deadliest day in the pandemic.

Officials renewed appeals for people with symptoms to get tested quickly.

Last week, the Victorian government said sick people breaking isolation rules - or not getting tested in time - was leading to continued spread despite lockdown measures.

"If you've got symptoms, the only thing you can do is get tested," said Premier Daniel Andrews.

"You just can't go to work. Because all you'll be doing is spreading the virus."

The result dashes hopes that lower case numbers in recent days meant the state had turned a corner.

However, Premier Andrews said Thursday's numbers also reflected the virus's hold in nursing homes in Melbourne - with one in six cases linked to residents and staff.

Elderly people have made up the majority of deaths reported in the past fortnight.

Due to a successful suppression of the virus in the first months of the pandemic, Australia has reported far lower case numbers than many other countries - with about 16,000 cases and 189 deaths.

However an outbreak in Melbourne, which began in June, has now led to more than 7,000 this month alone, accounting for about 95% of the nation's cases in the second wave.

Every other state has shut their borders to Victoria, while the city of Melbourne has made mask-wearing compulsory halfway through its six-week lockdown.

On Thursday, Premier Andrews also extended the face-mask policy to all of the state's residents from next Monday.

And alarm is also rising over the virus's spread in Sydney, after clusters emerged from travelling Melbourne residents.

Authorities warn the city is on a "knife's edge" where case rates could escalate if the virus spreads further in the community.

On Wednesday, Queensland joined the Northern Territory and Western Australia in barring entry to anyone from Sydney due to the renewed risk.