The dollar has weakened again, after data showing that US firms were hiring far fewer people than expected.
Investors are trying to calculate whether the dollar slide will persist
In response, the US dollar quickly lost its half-cent gain of the morning, sending the euro to a record $1.345 and strengthening the pound to $1.942.
US firms added just 112,000 new jobs during November, half the number that analysts had expected.
US stock markets rose regardless on Friday, after strong sales forecasts from giant semiconductor-maker Intel.
Intel is the world's biggest maker of microprocessors.
Europe's leading stock markets closed lower, with falls in London, Frankfurt and Paris. London's FTSE 100 index closed down 3 points at 4,747.
In New York, the Nasdaq index closed up 0.2% at 2,147 points, while the Dow Jones industrial average lost some of its early gains to close marginally higher at 10,592 points.
Economists warn that the dollar is likely to continue weakening, because of the so-called "twin deficits" of the US economy.
Both the US Government's budget and the current account - the measure of the difference between financial flows going in and out of the country - are deep in the red.
As a result, the US needs to suck in as much as $2.5bn in investment each day, creating a buyer's market for dollar assets and pushing the greenback lower.
Good news about jobs would have alleviated some worries about the health of the US economy.
But the expectation of more than 200,000 new jobs was disappointed.
But the unemployment rate, calculated by using a different survey sample, fell slightly by 0.1 percentage point to 5.4% the US Labor Department said.
On Thursday, the dollar fell to a fresh low against the euro, as talk of possible intervention on the currency markets by Europe and Japan was widely brushed off.
Both are seeing their exporters suffer as the euro and yen are pushed higher, and Japanese officials hinted that concerted action might be possible.
Announcing an unchanged euro zone interest rate on Thursday, European Central Bank president Jean-Claude Trichet refused to discuss intervention.
During Thursday, the dollar reached yet another record low against the euro, a five-year trough against Japan's currency of less than 102 yen, and its lowest level against the pound since before sterling was kicked out of Europe's exchange rate mechanism in September 1992.