Most markets for riskier assets have risen solidly this year - despite only modest global growth - due to robust corporate earnings reports, signs of an end to the euro zone crisis and renewed momentum in the US and Chinese economies.
But particularly in the equity markets, where many major indexes are close to multi-year highs, investors are looking for reassurance that a lasting economic recovery is underway.
"With markets posting significant gains for the year already, traders are becoming more demanding in their need for positive cues to keep up the buying momentum," said Jonathan Sudaria, a dealer at Capital Spreads in a trading note.
The FTSE Eurofirst 300 index of top European shares was up 0.2% in early trade after hitting a 23-month high on Monday. London's FTSE 100, Paris's CAC-40 and Frankfurt's DAX were flat to 0.1% higher.
US stock futures gained 0.1%, pointing to a firm Wall Street start.
Earlier the MSCI's broadest index of Asia-Pacific shares outside Japan rallied 0.9% to end a
The major event in investors' sights is the two-day Federal Reserve policy meeting. They are awaiting the Fed's decision and statement on Wednesday for any signs that the recent run of positive economic data would encourage policymakers to consider changing its easing policy.
The first estimate of US fourth-quarter gross domestic product also will be released on Wednesday, followed by non-farm payrolls on Friday.
In Europe, investors are looking at Spanish GDP data and Italian and German debt auctions on Wednesday, the first big day of European earnings on Thursday and the month-end.
Official data on China's growth outlook due Friday will also be important, especially for commodities markets.
Brent crude and US oil were edging higher on Tuesday but, in line with equities, gains were limited with Brent crude up 16 cents to $113.64 a barrel and US crude rising 44 cents to $96.88.
The euro was at $1.3450, not far from an 11-month high of $1.3480 hit on Friday when it had gained a boost from news of early repayments by euro zone banks of three-year loans to the European Central Bank, which suggested that parts of the banking system may be on the mend.
The euro, however, faces a series of major resistance levels near $1.35, including its 2012 high of $1.34869.
German government bond prices edged higher on Tuesday, as some investors were attracted by a dip that had followed Friday's announcement that banks would repay 137 billion euros of the ECB money.
Bund futures were 8 ticks higher on the day at 141.87. They hit a two-month low of 141.61 on Monday, having fallen by almost two full points in the past three sessions.