Australia's two most populous states, New South Wales and Victoria, will restrict public gatherings to two people from midnight, state leaders said on Monday, as part of a wave of new measures designed to slow the spread of coronavirus which has infected more than 4,000 across the country.

The two eastern states account for the majority of Australia's total COVID-19 infection cases and death toll, which stands at 16.

"It is only in exceptional circumstances that you should leave home," New South Wales Premier Gladys Berejiklian said in Sydney on Monday.

"We will get through this. We are in a position now which allows us to control the spread as much as possible."

Police in the neighboring state of Victoria will issue fines of 1,600 Australian dollars (984 U.S. dollars) to people who breach a limit of two people gathering in public, unless the group is from one household.

"Unless you want to be burying an elderly relative or your best mate, or your parents ... do the right thing," Victoria Premier Daniel Andrews said in Melbourne on Monday.

Confirmed COVID-19 cases breached the 4,000 mark overnight in Australia, although authorities said the rate of daily infections had halved in recent days.

All travelers arriving home in Australia from overseas now go into monitored quarantine in hotels or other facilities for 14 days, under police supervision, according to measures implemented at the weekend.

Australia has swayed in recent weeks between policies designed to keep as many businesses open as possible, and a more aggressive push to lock down the country, causing some confusion.

Amid concerns distressed assets could be snapped up by overseas buyers, Australia said on Monday that all foreign investment proposals would be assessed by the relevant government agency during the duration of the crisis.

While most virus cases have been detected in major cities, clusters have also emerged in tourist destinations, such as in the Barossa Valley, a wine region in South Australia.