The greenback slipped 0.83 percent to a near two-week low against the Swiss franc and fell to 110.11 yen, its lowest in nearly two months against the Japanese currency.
"Obviously we are looking at the increased tensions between the US and North Korea," said Brad Bechtel, managing director FX at Jefferies in New York.
"Tensions are still high and not going away at the moment. Safe havens are bid and markets are a little uneasy."
The dollar index, which tracks the greenback against six rival currencies, was up 0.07 percent to 93.717, after rising as high as 93.888 earlier in the session.
"The dollar is a safe haven, just as much as the Swiss franc and the yen. It shouldn't surprise that it's going to rally a little bit on this increased tension," said Bechtel.
Most Asian currencies stumbled, with the Korean won on pace for its biggest fall in nearly eight weeks as North Korea warned it is "carefully examining" plans for a missile strike on the US Pacific territory of Guam.
The warning came just hours after US President Donald Trump told North Korea that any threat it presented to the United States would be met with "fire and fury."
The Swiss franc was on pace for its biggest single-day rise against the euro since the Swiss National Bank removed its cap on the currency in January 2015.
Traders said hedge funds had cut leveraged bets against the franc, a traditional safe haven, prompted in part by worries about increased US-North Korea tension.
Against the dollar the euro was 0.16 percent lower.
"A combination of softer euro zone economic data, solid US reports and market positioning all resulted in a markedly heavier tone for the single currency," Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington, said in a note.
The bid for safe havens also pressured the Australian and New Zealand dollars.
Sterling was little changed against the greenback at close to a 2-1/2-week low, having lost around 2 percent since the Bank of England last week voted 6-2 to keep interest rates on hold at their record lows.