The dollar settled off 0.7 percent vs. the euro at $1.3615 Monday, after setting a new record low of $1.3638 in earlier trades. The euro had risen to $1.3554 as the dollar's slide continued in post-Christmas trading.
The euro's new high beat the previous mark of $1.3548 set on Friday in light trading.
The dollar has fallen steadily against the euro in recent weeks due to worries over the growing U.S. trade and budget deficits. Analysts expect the dollar to continue weakening and some have predicted the euro to hit $1.40 or higher by the end of 2005.
The dollar was last down 0.5 percent against the Japanese yen at 103.01.
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