Traders have taken comfort from very early hints that Omicron will be milder than feared as well as from remarks by President Joe Biden that the United States would not reinstate lockdowns.
At the same time, the World Health Organization warned of a "very high" risk of infection surges from Omicron, and countries around the world have reacted quickly to tighten border controls.
"The market wants to buy into the optimism that it's not going to be too bad, but every scientist - as opposed to economists pretending to be epidemiologists - is telling you its going to be a couple of weeks before we can draw that conclusion," said Ray Atrill head of FX strategy at NAB.
Global shares have also rallied, particularly in the U.S. and Europe.
This mood also helped the Australian dollar to eek out some gains rising to $0.7144, up from Monday's three month low of $0.7109, with an unexpected pick up in China's factory activity in November also a factor.
Sterling was little changed at $1.3324, while the euro also was flat at $1.1297.
The single currency slumped to a nearly 17-month trough of $1.11864 last week as European Central Bank policy makers stuck to their dovish stance in the face of heated inflation.
The latest reading on euro area consumer prices is due later Tuesday.
Prior to Omicron's arrival, the main driver of currency moves was how traders perceived the different speeds at which global central banks would end pandemic era stimulus and raise interest rates hoping to combat rising inflation without choking off growth.
In testimony prepared for Congress later Tuesday, Fed Chair Jerome Powell says Omicron could cause inflation pressures to last longer.
That would potentially speed the need for rate hikes, whereas traders initially reacted to Omicron's discovery by pushing back bets for Fed tightening because of the risk to growth.
Money markets currently see good odds of a first rate rise in July, but one is not fully priced until September.
Looming Fed rate hikes had previously been supporting the dollar.
"The dollar weakness we saw on Friday shows that a lot of the dollar strength was more a function of Fed thinking and Fed pricing. On any other day you would have expected the US dollar's safe haven credentials to have been prominent," Atrill said.
The dollar index, which measures the currency against six major rivals, last traded at 96.148, up from a low of 95.973 on Friday, when it suffered its biggest one-day drop since May.
China's yuan strengthened to a two-week high against the dollar on Tuesday and looked set to notch a fourth straight monthly gain, underpinned by persistent corporate demand and signs of liquidity tightness in the money markets.
(Reporting by Kevin Buckland and Alun John; Editing by Lincoln Feast.) ((Kevin.Buckland@thomsonreuters.com;))