 "Asian shares up, dollar slips as markets await data cues")
The euro, meanwhile, was hobbled by expectations that the European Central Bank will cut rates further, with a few tipping action as early as its policy meeting on Thursday
Eric Rosengren, president of the Boston Fed, said late on Monday that it may be appropriate to reduce the quantitative easing program when there is "compelling evidence of a sustainable recovery making satisfactory progress toward full employment.
Earlier on Monday, St. Louis Fed President James Bullard said the central bank need not rush because inflation remains low, while Fed Board Governor Jerome Powell said the tapering timing "is necessarily uncertain, as it depends on the evolution of the economy.
Australian shares rose 0.7% ahead of the conclusion of the Reserve Bank of Australia's policy meeting later in the session. The RBA will announce its decision at 0330 GMT and is widely expected to leave interest rates unchanged for a third month amid signs past cuts are filtering through to economic activity.
MSCI's broadest index of Asia-Pacific shares outside Japan added 0.2% in early trade.
US S&P E-mini futures were down about 0.1%, after the S&P 500 Index closed up 0.4% on Monday, just shy of a record high.
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The dollar index, which measures the greenback against six major currencies, slipped 0.2% to 80.582, though it remained well above a nine-month low of 78.998 hit on October 25.
The euro was slightly down from late US levels at $1.3508, moving back toward Monday's low of $1.3441, according to Reuters data. That was its lowest since September 18 and well below a nearly two-year high of $1.3832 set on October 25, as investors began to price in the likelihood of ECB easing action.
Money markets were already pricing in the possibility of looser ECB policy in the coming year and began to show a chance of a move even in the next few months, with a few big banks expecting a cut as early as this week.
A rate cut would hurt the euro's rate advantage over other currencies and make it less appealing for investors.
"We expect the ECB to leave its interest rates and forward guidance unchanged at Thursday's meeting," strategists at Barclays wrote in a note to clients.
"However, the latest decline in inflation has raised the likelihood that the main refinancing rate could be cut again by 25 basis points in December," they added.
The ECB last lowered its refinancing rate in May, to a record low of 0.5%.
Against the Japanese currency, the dollar was slightly higher on the day at 98.65 yen.
In addition to the ECB, investors will continue to focus on US data for clues on the timing of when the US central bank will begin to taper its monthly purchases of $85 billion in assets.
On Friday, the closely-watched October non-farm payrolls data will be released. Fed policymakers want to see the unemployment rate dropping closer to 6.5% from the current 7.2%, but economists in a Reuters survey expect the rate to have edged up in October to 7.3%.
Ahead of the jobs data, the third-quarter gross domestic product report will be released on Thursday. Those figures will help show how strong momentum was in the economy before last month's partial government shutdown.
Data on Monday showed orders for a wide range of US-made capital goods fell more than expected in September, suggesting companies cut their investment plans. But other recent data indicated that factory activity accelerated in October.