The euro was at $1.2771 in Asian trade, up from $1.276 late Monday in New York. The European currency had dropped to a low of $1.2665 in early Monday trade in Singapore.

The single currency was slightly higher against the Japanese unit at 98.11 yen, compared with 98.06 in New York.

The dollar edged down to 76.82 yen from 76.84.

French President Nicolas Sarkozy and German Chancellor Angela Merkel vowed Monday to speed up various measures to ease the eurozone crisis, saying an agreement on stricter budgetary rules tying in all EU members except Britain should be signed by March 1.

EU leaders are looking into ways of equipping the fund, the European Stability Mechanism, with all its resources in one go, rather than putting in smaller tranches under the current plan.

The meeting between the two leaders, who are at the forefront of efforts to combat the debt turmoil in the eurozone, came as the single currency flirted with new lows on the market amid signs of heightened banking tensions.

Investors will pay attention to how European shares react to the Sarkozy-Merkel talks, a senior dealer at a major bank in Tokyo told Dow Jones Newswires.

The dealer also said the euro may rise in Asia due to short covering as Asian investors hold "an amazing amount of short-euro positions".

Analysts also focused on a planned visit by US Treasury Secretary Timothy Geithner to Tokyo later this week.

Barclays Capital chief currency strategist Masafumi Yamamoto said the dollar may fall further against the yen if Geithner expresses any concerns regarding Japan's currency intervention.