"We have about 80 per cent of the cases ... in Australia that are either the result of someone who has contracted the virus overseas or someone who has had direct contact with someone who has returned from overseas," Prime Minister Scott Morrison told reporters in Canberra on Thursday.
Mr Morrison said the travel ban along with economic and health measures were aimed at "building a bridge".
"Our plan is to ensure that over the next six months, or as long as it then takes, that we then can effectively build a bridge to ensure that Australians, businesses, those impacted, we can bring them across the bridge and get them to the other side ... where the economy is rebounding and health is rebounding and Australian life can go back to what it was," he said.
The Reserve Bank on Thursday cut interest rates to a historic low of 0.25 per cent, while also providing extra support for banks to keep businesses alive.
It has set up a $90 billion fund to give banks more cash for loans while the government has tipped in an extra $15 billion for smaller lenders.
Central bank boss Philip Lowe sought to reassure people the virus would be contained at some point and the economy would recover.
"In the interim, a priority for the Reserve Bank is to support jobs, incomes and businesses, so that when the health crisis recedes, the country is well placed to recover strongly," he said.
So far, 636 people have caught coronavirus in Australia, and six people have died.
Non-essential indoor gatherings of more than 100 people have been banned, on top of a ban on outdoor events bigger than 500 people.
Tasmania has imposed the most dramatic lockdown in the country, requiring almost everyone entering the island state to go into quarantine for two weeks from Friday.
Health authorities are encouraging people to exercise "social distancing" measures, including standing 1.5 metres away from others and sitting in the back of taxis.
Restaurants, cinemas and other businesses will have guidance on how to put that into practice after the national cabinet meets on Friday morning.
Deputy chief medical officer Paul Kelly says health recommendations are based on a density of four square metres a person, but the practical applications would depend on the size of a room and how it is used.
Schools are staying open but strict restrictions have been placed on visitors to aged care homes to protect the elderly from contracting the virus.
Professor Kelly was confident the quarantine and social distancing measures would start to "flatten the curve" of the numbers of new people contracting the disease.
"When it will actually start to decrease like that ... I don't have a crystal ball," he told reporters.
"In the meantime, we're looking to find our cases, get them to stay at home, to find their contacts, get them to stay at home and to flatten the curve."
Mr Morrison again urged people not to panic-buy groceries and other goods.
"There are no issues with Australia's food supply. What there is an issue with is the behaviour of Australians at supermarkets," he said.
"I understand they're anxious ... but for the next six months at least we need to work through this together."
The government has imposed buying restrictions on some medicines, including children's paracetamol and asthma inhalers such as Ventolin, to make sure people aren't stockpiling them.
Pharmacists will also be required to limit some prescription-only medicines to dispensing one month's supply at a time.
Opposition Leader Anthony Albanese urged the government to be transparent about what further restrictions could be placed on daily life.
As of Tuesday afternoon, only people who have recently travelled from overseas or have been in contact with a confirmed COVID-19 case and experienced symptoms within 14 days are advised to be tested.
If you believe you may have contracted the virus, call your doctor, don’t visit, or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.