Against the yen, the US currency traded at 110.37 yen , gaining 0.1% in Asia on Japanese buying before month-end but still almost two full yen below its 10-month high touched last Thursday.
The euro fetched $1.08815, extending its rebound since it hit near three-year low of $1.0778 on Thursday.
The dollar had risen until last week as investors had regarded the United States as less exposed to the coronavirus and believed its economy more resilient than other major economies, making US assets a safe harbour.
Growth in China looks set to fall further from a three-decade low of 6.1% last year after the outbreak caused massive economic disruptions, while both the euro zone and Japan are seen on the brink of recession.
Such convictions have started to crumble, however.
A top official at the US Centers for Disease Control and Prevention (CDC) urged Americans to begin preparing for coronavirus to spread within the country, while another official said it was no longer a question of if, but when, the virus would become a pandemic.
As outbreaks started to quickly spread to the Middle East and Europe, investors no longer saw the US economy immune and
started to bet the US Federal Reserve will have to cut interest rates to support the US economy.
US money market futures now fully price in a 0.25 percentage point cut by the end of June, compared to about 50% chance a week ago, although Fed officials have shied away from indicating a policy move.
Fed Vice Chair Richard Clarida said late on Tuesday the Fed is "closely monitoring" the escalating coronavirus outbreak but it is still too soon to gauge if it would require a change in monetary policy.
Still the 10-year US Treasuries yield plunged to a record low near 1.30%, reducing the dollar's relative yield attraction.
In contrast to the Fed, the world's other major central banks such as the European Central Bank and the Bank of Japan have limited room for easing with their policy rates already at record lows.
"Markets had been under-estimating the risk of coronavirus but I think that phase is over by now," said Tatsuya Chiba, manager of forex at Mitsubishi Trust Bank.
Chiba said the risk-off mood is likely to linger for another month or so until the market reach the extreme in the opposite direction by over-estimating the risk.
"I would think we will see the peak of fears when people become seriously worried about an epidemic in the United States."
The risk-sensitive Australian dollar stood at $0.6603 , stuck near Monday's 11-year low of $0.6585.