The euro hit US$1.3453 in morning trading, edging above the previous record of US$1.3452 it set on Friday.
Since September, the shared European currency has spiked from around US$1.20 over persistent concerns about the U.S. trade and budget deficits.
It broke the US$1.34 mark for the first time on Friday when U.S. employment data came in weaker than expected.
The ripple effect of the shrinking dollar is also being seen among OPEC producers, who are to meet in Cairo Friday and are expected to bolster oil prices by approving a cut in production.
A weak dollar hurts exports to the United States - the world's largest energy consumer - and world leaders are concerned their currencies' rapid rise will have a major impact on their sales, and ultimately on their purchasing power.
Monday, the price of crude oil edged higher in Asia on Monday, but stayed below the US$43 per barrel threshold as concerns over supplies continued to ease.
By mid-afternoon in Asia, benchmark light, sweet crude rose 23 cents to US$42.77 per barrel on the New York Mercantile Exchange from its Friday closing.
Crude prices fell Friday for a fourth straight day to sit below US$43 per barrel for the first time in three months - capping a 14 percent fall for the week.
"The dive in oil prices is welcome news for consumers. Producers have less to celebrate," said Eneryintel's Peter Kemp in a research note.
"That's not because they believe US$50 oil is desirable or sustainable. It's because the value of the dollar is collapsing. The 35 percent decline of the U.S. currency against the euro over the past three years has hammered the purchasing power of OPEC producers."
Prices peaked in late October, settling twice at US$55.17 per barrel.
"We have a huge amount of oil in the market and on the sea," Iran's Oil Minister Bijan Namdar Zanganeh told Dow Jones Newswires Monday. "OPEC really should be worried if it keeps on overproducing," he added, pushing for members to stick to its quotas.
"OPEC needs to start cutting supply by 500,000 barrels a day now, and then cut again when the price reaches US$35 a barrel," Libya's Oil Minister Fathi bin Shatwan said.
Petroleum prices have been high all year due to strong global demand, a tight supply cushion and fears of output disruptions in Iraq, Nigeria and Russia. In September, Hurricane Ivan knocked out significant oil production in the Gulf of Mexico, though the region's output is now recovering.
The price of oil is still around 40 percent higher than a year ago, putting the greatest financial pressure on low-income families, chemical manufacturers and the airline industry.