MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.3 percent in early trade, while Japan's Nikkei stock average was up 0.4 percent ahead of a Japanese holiday on Tuesday.
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"U.S. data over the next three weeks are likely to underline the outperformance of the U.S. economy and provide broad support" for the U.S. dollar, strategists at Barclays wrote in a note clients on Monday.
On Wall Street on Friday, U.S. shares rose, with the S&P 500 coming within a few points of its closing record high. That index gained 5 percent since Wednesday to log its best three-day gain since 2011, after the U.S. Federal Reserve said it would be "patient" on raising benchmark U.S. interest rates, depending on domestic growth and inflation.
Three Fed officials on Friday offered clues on the thinking inside the U.S. central bank as it gears up to raise interest rates, likely in 2015.
Richmond Fed President Jeffrey Lacker echoed Fed Chair Janet Yellen's view at her press conference two days earlier that the drop in energy prices will boost U.S. consumer spending, and said that he supported the central bank's addition of the word "patient" to describe its interest rate guidance in its policy statement last week. Minneapolis Fed President Narayana Kocherlakota said rate hikes in 2015 would create "unacceptable" downside risks to U.S. inflation.
San Francisco Fed chief John Williams told Bloomberg Radio it seems "reasonable" for the Fed to raise rates in mid-2015.
In contrast, ECB governing council member Luc Coene said in a newspaper interview on Saturday that the bank should start buying government bonds to tackle poor investor confidence and low inflation in the euro zone.
The euro edged down to $1.2224 , dropping as low as $1.2220 earlier, its lowest level since August 2012.
Against the yen, it edged slightly up to 146.07 yen , but remained a considerable distance from a six-year high of 149.79 touched earlier in December.
Calming some fears about political stability in the euro zone, Greek Prime Minister Antonis Samaras offered on Sunday to bring pro-European independents into the government and hold new elections in late 2015 if lawmakers back him to elect a new president.
Against the yen, the dollar was flat on the day at 119.50 , still well off a 7-1/2 year high of 121.86 touched this month but off last week's low of 115.56 marked before the Fed's statement.
On Friday, the Bank of Japan maintained its pledge of increasing base money, or cash and deposits at banks, at an annual pace of 80 trillion yen ($669.40 billion) through aggressive asset purchases. Governor Haruhiko Kuroda voiced confidence the bank will meet its ambitious price target despite a recent plunge in oil prices.
Oil took a breather on Monday after its recent gyrations, with U.S. crude edging up 0.1 percent to $57.20 a barrel, following a week in which it shed 2 percent lower to extending its recent rout that has nearly halved its value since June.
($1 = 119.5100 yen)