The recovered slightly from a two-month low against the dollar on Monday, helped by higher short-term market interest rates, although speculation the European Central Bank may step in limited its gains.
After breaking through support at $1.3550 on Friday, the euro fell in Asian trading on Monday, touching its lowest since November 25 at $1.35080. It later recovered some ground, and was 0.1 percent higher at $1.3550 early in London.
The single currency has weakened this month as year-end factors such as euro zone banks repatriating assets fade, with speculation the ECB will act to loosen liquidity meaning that even a rise in overnight borrowing rates has failed to lift it.
"We think that (the) key driver of the recent euro under performance is growing market expectations of ECB action to address the tightening money market conditions," said Citi strategist Valentin Marinov.
(Read more: ECB'S Draghi sees nourgent need to cut rates further)
Eonia, the euro zone overnight bank-to-bank lending rate, rose above 0.30 percent on Friday, more than the headline 0.25 percent rate that banks pay when they borrow at the ECB's still unrestricted lending operations.
After the central bank's January policy meeting, ECB President Mario Draghi said an"unwarranted" rise in the bank-to-bank lending rates that underpin euro zone borrowing costs would be one of the triggers for another rate cut or more drastic action.
One trader said the euro's rise may squeeze out some short-sellers but that the single currency could then head lower again, potentially entering a technical downtrend.
"The market has been focusing on broad dollar strength against everything except the euro ... The euro was playing catch-up," said Chris Turner, head of FX strategy at ING, referring to the euro's overnight weakness.
(Read more: Euro zone manufacturing grows; France stumbles on)
Turner said he expects the euro to fall to $1.33 this week and to $1.20 by the end of the year against a strengthening dollar as the Federal Reserve cuts back its huge bond-buying program and as euro zone residents begin to invest abroad.
Investors were left looking for direction, with little economic data due out of Europe, other than German December producer prices that were slightly above forecast.U.S. markets are closed on Monday for Martin Luther King day.
The Australian dollar got some relief after China's annual economic growth in the final quarter of 2013 came in at 7.7 percent, down from 7.8 percent in the previous three months but slightly ahead of market expectations for growth of 7.6 percent.
"It's not a particularly good number but there wasn't any drop to levels below the 7.5 percent threshold," said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation.
While the data might have spurred some short-covering in the Australian dollar, the impetus is unlikely to be strong enough to prompt traders to go long the currency, he added.
(Read more: What's next for China? Economists are split)
The Aussie edged up 0.1 percent on the day to $0.8790 after earlier falling to $0.8756, its lowest level in about 3 1/2 years, in the wake of weak jobs data last week.
Traders said the 87 U.S. cent area should provide good support, as it did in 2010, although a break could see it test $0.8600 in a hurry.