The dollar index increased 0.1% to 98.091, while the euro was down 0.2% versus the US currency at $1.1001 , not far from its Tuesday low, which was its weakest since early Nov. 29.
The greenback is now up 1.8% against a basket of major currencies so far in 2020, ahead of a Federal Reserve meeting later on Wednesday.
The Fed is not expected to change interest rates when it gives its decision at 1900 GMT, but investors will want to hear whether chairman Jerome Powell retains his cautiously upbeat language.
ING analysts said that with the market already pricing in another 25 basis point rate cut from the Fed in 2020, the dollar looked like it would hold recent gains.
"With dovish pricing already in place, the bar for a dollar decline vs low yielding currencies such as JPY or EUR remains high," they wrote in a research note.
The yen, which jumped earlier this week as investors bought into a currency considered a safe store of value in times of stress, traded up 0.1% at 109.06 yen per dollar.
The Swiss franc rallied 0.1% to 1.0720 francs per euro, some way off Tuesday's nearly three-year high of 1.0666.
"The dollar is the outperformer and illustrates in an impressive manner who is the ultimate safe haven in the FX universe - regardless of whether that is justified or not," Commerzbank analyst Antje Praefcke said.
The newly identified coronavirus has created alarm because it is spreading quickly and there is little known about it. The death toll rose sharply to 132 on Wednesday, with nearly 1,500 new cases identified for a total of nearly 6,000.
While there was evidence that investors were becoming more relaxed about the likely economic impact of the virus, especially in China, concern remained elevated.
The offshore yuan - heavily sold in recent days - initially rose but by 1145 GMT stood at 6.9635 per dollar, unchanged on the day. On Monday, it had fallen to 6.9900 yuan per dollar, its weakest in almost a month.
Sterling fell 0.1% to $1.3012 ahead of a Bank of England meeting on Thursday. Investors are divided as to whether it will cut rates.
Australia's dollar briefly extended its rebound from 3-1/2 month lows after firmer-than-expected inflation data. The Aussie then succumbed to selling pressure and was last down 0.2% at $0.6748.