Rate cuts are inflationary, lowering the value of the dollar.
Expectations that the Fed will cut rates at least 25 basis points at its June meeting were at 78.3% on Tuesday, according to CME Group's FedWatch tool.
The same tool shows a 4.1% chance that rates will be in the current 150-175 basis-point range in December, down from 28.6% a month ago.
"The potential for the economic fallout from the virus to wash up on US shores has cooled the dollar's rally to three-year peaks by knocking Treasury yields to multi-year lows and raising expectations for the Federal Reserve to deliver more interest rate cuts to keep the record long expansion intact," said Joe Manimbo, senior market analyst at Western Union Business Solutions.
Against a basket of six other currencies the dollar slipped 0.401% to 98.939, after reaching a three-year high of close to 100 last week.
The index fell in step with the benchmark 10-year Treasury note yield, which hit an all-time low, driven by safe-haven demand. That flight to safety also saw US stock indexes fall, with Wall Street's three major indexes down almost 2% on Tuesday.
The US Centers for Disease Control and Prevention (CDC) on Tuesday alerted Americans to begin preparing for the spread of coronavirus in the United States after the flu-like virus surfaced in several more countries.
Versus the euro, the dollar was modestly weaker, last down 0.28% at $1.088. Market gauges of implied volatility in euro/dollar eased on Tuesday after rising to their highest level since October on Monday.
The yen was 0.61% stronger at 110.04 per dollar.
China's yuan was last up 0.11% at 7.028 per US dollar in the offshore market, after rising to a five-day high earlier in the session.