Other Asian stock markets were mixed after the Dow surged more than 5% on hopes of fresh support.
Shares in Japan have fallen over concerns that world governments and central banks won't do enough to tackle the economic impact of the coronavirus.
It comes despite stock markets bouncing back in the US and Europe on hopes that authorities will work together to support markets.
The Dow Jones surged 5.1% overnight, after more modest gains in Europe.
The rebound followed the worst week for major stock markets since the 2008 financial crisis.
Japanese shares closed 1.2% lower due to concerns that Group of Seven (G7) countries may not announce a detailed and coordinated response to limit the economic damage from the outbreak.
The G7 is expected to release a statement later today or tomorrow as policymakers struggle to respond to the global spread of the virus, but there are concerns that it may not mention any new government spending or coordinated interest rate cuts.
Investors have been worried about the impact of the coronavirus as it spreads outside of China. Already, the outbreak has led to travel restrictions, manufacturing shortages and reduced shopper demand in some countries.
On Tuesday Australia's central bank cut interest rates to record lows, in what is expected to be the first in a spate of stimulus measures around the world to fight the economic impact of the coronavirus outbreak.
Reserve Bank of Australia governor Philip Lowe said: "The board took this decision to support the economy as it responds to the global coronavirus outbreak."
It comes after central banks in the UK, US, Europe and Japan made statements aimed at calming fears following last week's market turmoil.
"The Bank is working closely with HM Treasury and the FCA (Financial Conduct Authority) - as well as our international partners - to ensure all necessary steps are taken to protect financial and monetary stability," a Bank of England spokesman said.
The European Central Bank said it was "closely monitoring developments and their implications for the economy, medium-term inflation and the transmission of our monetary policy".
"We stand ready to take appropriate and targeted measures, as necessary and commensurate with the underlying risks," it said.
The US Federal Reserve put out a similar statement last week.
The comments come as economic groups revise growth forecasts to account for the virus.
On Monday, the Organisation for Economic Cooperation and Development (OECD) said it expected growth of just 2.4% in 2020, down from 2.9% in November and warned that a longer "more intensive" outbreak could halve growth to 1.5%. BBC