Versus the euro, the dollar was up, although still above $1.08, a key level it broke last week. Euro/dollar was last down 0.1% at $1.0839.
Market gauges of implied volatility in euro/dollar eased on Tuesday after rising to their highest since October on Monday.
Japanese Prime Minister Shinzo Abe said on Tuesday that clusters of coronavirus cases had emerged in the country and that the government would take stronger steps to fight contagion. That gave Asian investors another reason to avoid the yen, which had been losing its safe-haven status recently.
The yen last traded up 0.2% at 110.47 per dollar.
China, meanwhile, reported a rise in new coronavirus cases in Hubei province, the epicentre of the outbreak, but the rest of the country saw a fourth straight day of declines.
South Korea, which has the most virus cases in Asia outside China, reported 60 new cases on Tuesday, increasing its total to 893 - leaving few to expect the region's currencies to do more than hold steady for now.
China's yuan was last up 0.1% at 7.0280 per US dollar in the offshore market, after rising to a five-day high.
The virus has continued to spread in Italy and Iran. Health ministries in the most affected countries urged people to stay at home.
Lee Hardman, currency analyst at MUFG, said he expected "some downside risk for the US dollar", given the Fed's potential dovish shift in policy. Expectations for further Fed easing continue to build, with money markets pricing in a 25- basis-point cut for the meeting in June.
For the year as a whole, traders expect the central bank to cut rates to between 1% and 1.25% from the current 1.5% to 1.75% range.