The euro fell to its weakest since mid-April against the dollar, before a European Central Bank meeting on Thursday that is expected to unveil fresh monetary easing measures.
The Federal Reserve, by contrast, is expected to raise US interest rates in December for the first time in nearly a decade. Reflecting the policy divergence, the gap between US and euro zone two-year bond yields reached its widest in nine years.
The prospect of more ECB stimulus, via an extension of its bond-buying programme, lifted European shares. Wall Street was expected to open modestly higher, according to stock index futures.
Oil prices, a major driver of markets this year, rose as investors took positions before an OPEC meeting on Friday that is not expected to change its output policy, which has led to a glut in supply.
The ECB is widely expected to cut its already negative deposit rate by at least 10 basis points and extend its asset-purchase programme, which currently stands at 60 billion euros a month.
"The market expects a broadening of the purchase programme as well as a cut in the deposit rate, but expectations have gone quite far since we had rumours last week of a possible two-tier deposit rate cut," said Norbert Wuthe, rate strategist at Bayerische Landesbank.
The dollar index, which measures the greenback against a basket of currencies, touched its highest since mid-March and was on track for a 3% gain on the month.
The euro fell 0.2% to $1.0566 while the yen lost 0.2% to 123.05 per dollar. Sterling hit a seven-month low just below $1.50.
"We are probably with the consensus, the Fed is going to tighten, the ECB is going to ease, so the euro will go lower to about 1.05 and then that will be your lot (for the year)," said Sanjiv Shah, Chief Investment Officer with Sun Global in London.
The pan-European FTSEurofirst 300 index was last up 0.5%.
"There is still some optimism ahead of the ECB meeting on Thursday, which is the key market driver of the week," said Carlo Alberto De Casa, analyst at ActivTrades in London.
Earlier, shares fell in Asia. MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.8% and was on course to lose about 2.8% for the month of November, after making its first gains in six months in October.
Chinese stocks, which fell more than 5% on Friday, were at one point down a further 3% on Monday before closing marginally up on the day. The CSI300 index of the largest listed companies in Shanghai and Shenzhen and the Shanghai Composite both ended up 0.3%.
China's currency was also in the spotlight, with the yuan jumping in offshore trade on suspected intervention by Beijing, hours before the International Monetary Fund is expected to grant it reserve status. It last traded at 6.431 to the dollar, up 0.2% on the day.
Tokyo's Nikkei stocks index fell 0.7% on concern over China and after Japanese industrial output data undershot forecasts.
Global benchmark
Brent crude, the global benchmark for oil prices, rose 45 cents to $45.31 per barrel. It remained on track for a 10% fall this month.
While most analysts do not expect OPEC to cut output, they are mindful that Saudi Arabia could be inching towards the idea of working on price support measures with other oil producers.
Gold, which has fallen lately on the prospect of higher U.S. interest rates, was on track for its worst month in 2 1/2 years. It last traded down 0.1% at $1,056.40 an ounce.
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