At 1120 GMT, the FTSEurofirst 300 index of top European shares was up 0.2 percent at 1,274.71 points, failing to bounce back convincingly from last week's 3.5 percent slide.
Late on Monday, St. Louis Fed President James Bullard, a voting member on the US central bank's policymaking committee, said the Fed could reduce its monthly bond purchases slightly this month, sooner than most economists expect.
"Stocks are struggling to bounce back towards year-highs because investors are petrified by the prospect of less liquidity from central banks," said Guillaume Dumans, co-head of research firm 2Bremans.
"With the year almost over, more and more investors are cutting their positions instead of just putting stop losses. They want to preserve their annual performance."
Stocks have rallied strongly this year, with the FTSEurofirst 300 up 12 percent. But the run-up stalled in late October following a raft of lower-than-expected corporate results and on mounting expectations that the Fed would soon start to trim its $85 billion a month of bond buying.
"It's 'wait-and-see' until the Fed's policy meeting next week, although there is still room on the downside," Global Equities head of quantitative sales trading David Thebault said.
"The best thing to do is to prepare a list of stocks you want to buy, and when the market further drops, it will be time to scoop up the shares."
Heavyweight miners were among the top losers on Tuesday, with BHP Billiton down 1.1 percent and Vedanta Resources down 1.5 percent. Dutch oil and chemicals storage firm Vopak fell 2.8 percent after warning about its outlook.
Around Europe, the UK's FTSE 100 index was up 0.2 percent, Germany's DAX index up 0.2 percent and France's CAC 40 up 0.1 percent.
The euro zone's blue chip Euro STOXX 50 index was up 0.2 percent at 2,996.34 points.
After failing to break above an October peak around 3,100 points, the index sharply fell last week, losing nearly 5 percent and falling below its 50-day moving average, which sent a negative technical signal.
"From a short-term perspective, the index concluded its June uptrend with a profit-taking signal and entered a consolidation, which should continue in the coming days," Sophia Wurm, technical analyst at Commerzbank, said.