The remarks were the catalyst for broad-based losses in the US currency which tumbled to multi-week lows against most major currencies, seven-year lows against the Korean won and 22-year lows against the New Zealand dollar.
"The market used the Korean diversification story as evidence to fit the crime," said Neal Kimberley, head of FX sales at Bank of Tokyo-Mitsubishi. "The dollar went through some chart levels and it became self-fulfilling."
At 1240 GMT the euro was up just over one percent at $1.3210 having accelerated on the break of resistance levels at $1.3090 and $1.3200. Data showing the euro zone's trade surplus widened to 5.7 billion euros in December gave the euro additional support. The dollar was down 1.5 percent at 104.00 yen, on track for its biggest one-day fall since last October.
North Korea's offer to return to six-party talks on nuclear disarmament and moves by China to allow companies to keep more foreign exchange income - a step towards greater exchange rate flexibility - also boosted the yen.
Many traders said the market was looking for an excuse to sell the dollar after being caught off-guard by the currency's rebound at the start of 2005.
The dollar's inability to capitalise on upbeat US economic data last week had already fuelled suspicions that its New Year rebound had run out of steam.
"The comments from Korea came at a time when sentiment towards the dollar was already softening," said Ian Gunner, head of foreign exchange reserve at Mellon Financial.
"When the dollar broke through sell stops, it generated its own momentum."
Bahrain's central bank governor told Reuters on Tuesday he saw a growing role for the euro in international reserves as Europe's economy starts to grow and capture a bigger part of world trade.
He added however the bank was in a no hurry to diversify away from the falling dollar.
The dollar's slide comes as the market looks to US consumer price inflation data due on Wednesday for any hint that accelerating price pressures could prompt the Federal Reserve to step up the pace of its credit tightening campaign.
Expectations for steady rises in US interest rates have eased concerns about funding the US current account deficit and helped the dollar recover from record lows against the euro set in the final days of last year.