By William L. Watts, MarketWatch

FRANKFURT (MarketWatch)--The dollar gave back some of its recent gains Monday as investors grew cautiously upbeat over efforts to avert the so-called fiscal cliff, robbing the currency of haven-related support.

The ICE dollar index (DXY), which measures the U.S. unit against a basket of six major rivals, dipped to 81.020 from 81.286 in North American trade late Friday. The index rose 0.5% last week.

"Despite a push back into long U.S. dollar positions last week, on a one-day view the greenback is the weakest performing G-10 currency," said Jane Foley, senior currency strategist at Rabobank International in London. "Hope that U.S. politicians can avoid the fiscal cliff has been gaining traction over the weekend."

After a Friday meeting at the White House, top congressional Republicans and Democrats were both upbeat on prospects for averting the automatic round of billions in tax hikes and spending cuts due to take effect in January. Economists fear the measures could eventually drag the U.S. economy back into recession unless politicians reach a budget deal.

"I am confident we can get our fiscal situation dealt with," President Barack Obama told a news conference Sunday in Bangkok, where he started a three-nation Asian trip. .

Global equities traded higher to begin the week and U.S. stock index futures followed suit, with investors citing the encouraging, albeit vague, remarks from key players. .

The WSJ Dollar Index , which tracks the dollar against a slightly wider basket, eased 0.18 point to stand at 70.80.

Overall activity this week will likely be light and potentially choppy, with U.S. markets closed Thursday for the Thanksgiving Day holiday, strategists said.

The euro changed hands at $1.2776, up from $1.2624 late Friday. The British pound traded at $1.5906, up from $1.5882.

Tuesday meeting on Greece

The euro, and overall risk appetite, may be vulnerable to developments surrounding Greece. Euro-zone finance ministers will meet for the second time in two weeks on Tuesday in an effort to overcome differences with the International Monetary Fund over how to get Greece's debt load back on a sustainable track.

"While [finance ministers] may attempt to contain the Greek question tomorrow, the issue of IMF acceptance and the funding of the deficit maturity extension remain uncertain," leaving euro rallies "worth fading," said Jeremy Stretch, strategist at CIBC in London. He expects the euro to reverse back toward the 100-day moving average at $1.2650.

Technical resistance is seen at the 200-day moving average at $1.2808, analysts said.

The dollar also bought 81.14 Japanese yen, down from  ¥81.19 late Friday.

The U.S. unit soared to a six-month high on the yen last week as Shinzo Abe, the leader of the main opposition Liberal Democratic Party, repeated a vow to push the Bank of Japan to undertake what would be much more accommodative a monetary stance. .

Abe is seen as likely to become Japan's next prime minister after elections scheduled for Dec. 16.

Meanwhile, attention turned to the Tuesday conclusion of the Bank of Japan's two-day policy meeting, which will be closely watched for signs that further monetary easing is in the works. .

Also Monday, the Australian dollar rose to $1.0393 from $1.0325, while the U.S. unit fell 0.3% versus the Canadian dollar to trade at 99.83 Canadian cents.

The IMF is set to formally classify the Australian and Canadian dollars as official reserve assets, which over time could have a significant impact on global bond and equity markets. .

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