The single currency did recover some of its losses in European trading but traders and analysts said the rush by investors unwinding their short positions on the greenback was unlikely to be over.
Concerns about the US exit from an international nuclear deal with Iran had also supported the dollar in early Asian trading.
"It's a continuation of what we have been witnessing for the past few weeks," said Christin Tuxen, FX strategist at Danske Bank. "There might have been a bit of safe haven flows but overall it's to do with the US holding a favourable cyclical position."
While there was talk of investors seeking out safe havens on Tuesday ahead of US President Donald Trump's announcement of a withdrawal from the nuclear deal, on Wednesday the Swiss Franc barely budged versus the euro and the Japanese yen fell to a one-week low as the dollar gained half a percent.
Trump's decision to exit the accord was most keenly felt in oil markets, where prices rallied.
The three-week long rally for the US currency, in which it has reversed several months of weakness, is dominating currency markets this week and has caused the unwinding of popular trading positions across emerging markets and in the 'G10'.
US Treasury rates have crept higher in recent weeks on expectations the Federal Reserve will tighten policy to combat inflation amid a huge government injection of fiscal stimulus under Trump.
Forecasts for rising rates in the euro zone, by contrast, are being pushed back. Euro zone money markets now price roughly a 75 percent chance of a 10 basis point hike from the European Central Bank by mid-2019, scaling back bets on a rate rise given a softening in economic data and inflation.
After falling 0.3 percent to $1.1823 versus the dollar, its lowest in 2018, the euro recovered to trade up 0.2 percent at $1.1883.
The euro has lost one percent of its value in May as investors betting on a falling dollar were caught out and rushed to cover their positions, further pushing the greenback higher.
The dollar index fell 0.2 percent from a 2018 high to 92.959 .
Against the yen, the dollar rose half a percent to 109.675 .
Trump on Tuesday pulled the United States out of the deal with Iran, raising the risk of conflict in the Middle East, upsetting European allies and casting uncertainty over global oil supplies.
Sentiment towards the euro cooled after Italian President Sergio Mattarella's call to bickering political parties to rally behind a "neutral government" were met with immediate opposition and raised the prospect of elections being held as early as July.
"Solid US inflation data tomorrow and the expected dovish comments of ECB President Mario Draghi in Florence on Friday following the recently disappointing data from the euro zone point towards a continuation of the downtrend in euro/dollar," Commerzbank analysts said in a note.
The Swedish crown, one of the worst performing G10 currencies in 2018, moved sharply higher as investors unwound positions. The crown rose 1 percent against the dollar and 0.9 percent against the euro.
The Swiss franc, traditionally a safe-haven currency, fell 0.1 percent versus the dollar but gained 0.1 percent against the euro. It had hit a three-week high against the euro on Tuesday.