Analysts say the steady depreciation not only remains orderly, but also carries the potential to help America get its whopping trade and current account deficits - which are widely criticised in Europe - back into better balance.
"I think on balance there are far more positives for the United States in what is going on in currencies than there are negatives," said economist Greg Valliere of Schwab Washington Research Group.
The euro broke above the $1.25 barrier for the first time on Monday, and late on Tuesday was trading at around $1.2550.
The euro's strength and the dollar's dive come before a 6-7 February meeting in Boca Raton, Florida, of the Group of Seven finance ministers where currency issues are always discussed.
The G7 consists of the United States, Britain, Canada, France, Germany, Italy and Japan.
US endorses fall
In just under a year since taking office last January, Treasury Secretary John Snow has toned down the former hard-line US commitment to a "strong dollar," effectively endorsing the fall by saying its value "reflects the fundamentals of the demand and supply for currencies".
Snow replaced former Treasury Secretary Paul O'Neill, who resigned under White House fire before Christmas last year.
"It makes sense, given that inflation has been low and interest rates are at low levels, so under those circumstances a logical response would be to favour a weaker dollar"
"Long term, the weakness of our trade and current account imbalances meant we had to reverse course (on currency policy) so what we're seeing is a natural process and not something that should cause a lot of alarm," said Greg Mastel, an international trade adviser with Washington law firm Miller and Chevalier.
"It makes sense, given that inflation has been low and interest rates are at low levels, so under those circumstances a logical response would be to favour a weaker dollar," Mastel added, since it means there is little or no risk of importing price pressures and a better chance of boosting US exports.
Economist Allen Sinai of Decision Economics Inc in Boston wrote this week that the Bush administration had an evident policy of "benign neglect, if not outright approval" of a cheaper dollar.
He added the US stance was a legitimate one.
"It is patently clear that the administration does not mind a declining dollar, so long as it is 'orderly'," Sinai said.
"At this stage, a lower dollar should increase exports, help manufacturing, increase US economic growth, not be a problem for inflation and if financial troubles occur, they would only do so from time to time," Sinai said.
Valliere similarly said that he saw no indication of official unease over the dollar weakening, possibly because there seemed to be no likelihood of a surge in inflation as can happen when a cheaper dollar makes imports more costly.
"The more relevant point might be whether the Europeans or Japanese start to cry 'uncle' and ask for coordinated intervention or for Snow to at least say the dollar slide has gone far enough," Valliere said.
"But frankly, I don't see any sign that this is becoming a major issue for Washington," he added.