The euro has risen to $1.2861 from $1.2769 last night and is on course to hit last month's record high of $1.2890.
The latest surge follows European Central Bank president Jean-Claude Trichet's statement on Monday that that the bank was not overly concerned about the strength of the euro.
Not all eurozone members share this view however, with Germany in particular expressing its concerns, while others are worried about the impact on European exports that a rising currency will have.
Analysts believe that the market is using the comments to see if the ECB will intervene to halt the appreciation.
Sterling also rose sharply, breaking through the $1.90 mark for the first time since 1992.