Brent crude prices marked their biggest decline in more than three years on Tuesday and U.S. and German debt attracted buyers on lingering anxiety over world economic growth.

Wall Street struggled to maintain gains, after rising more than 1 percent earlier, as energy shares slid to enter a bear market.

Worries about a slowing global economy and fears of the spread of Ebola have made investors skittish of late. The CBOE Volatility Index, the equity market's preferred gauge of anxiety, edged lower but still closed at its second-highest level in more than two years.

An MSCI gauge of major stocks worldwide .MIWD00000PUS was down 0.15 percent after hitting an eight-month low earlier.

Investors have turned more defensive due to worries about the U.S. Federal Reserve ending its bond-buying stimulus later this month, mounting risks of recession in the euro zone, and a floundering Japanese economy.

The German Economy Ministry sharply cut its forecasts for growth for 2014 and 2015, and business sentiment also fell in Europe's largest economy.

Benchmark U.S. Treasuries yields US10YT=RR fell as low as 2.176 percent, the lowest level in 16 months, while yields on German 10-year debt DE10YT=TWEB touched a record low of 0.836 percent.

"You've seen global growth expectations come down a lot so yields in Europe are way down," said Court Hoover, director of research at JA Forlines Global Investment Management in Locust Valley, New York.

"Even if some of the data in the U.S. isn't looking all that bad, the fact that Europe is likely going back into recession, Japan is going back into recession, that drags down U.S. yields in sympathy and that process can continue."

The U.S. bond market was closed on Monday for the Columbus Day holiday.

Brent crude settled down 4.3 percent, the most for a single day going back to September 2011, after the International Energy Agency cut estimates for oil demand this year and next. Brent touched its lowest price since November 2010.

"Recent price drops appear both supply and demand driven," the IEA said in its monthly oil market report. "Further oil price drops would likely be needed for supply to take a hit, or for demand growth to get a lift."

Brent futures LCOc1 last traded down 4 percent at $85.32 a barrel, having hit a low of $84.48. U.S. crude CLc1 fell 4.2 percent to $82.12.

On Wall Street the S&P 500 gave up a gain of 1 percent after falling 4.8 percent in the previous three sessions. Stocks managed to hold on to smaller gains as focus shifted to corporate earnings but the large drop in oil prices pummeled energy shares.

The Dow Jones industrial average .DJI fell 5.88 points, or 0.04 percent, to 16,315.19, theS&P 500 .SPX gained 2.96 points, or 0.16 percent, to 1,877.7, and the Nasdaq Composite.IXIC added 13.52 points, or 0.32 percent, to 4,227.17.

Citigroup (C.N) was the S&P 500's biggest point gainer, closing up 3.1 percent at $51.47 after reporting quarterly results that exceeded estimates.

"I think this market action today points to further declines ahead in the short term," said Peter Cardillo, chief market economist at Rockwell Global Capital in New York:

"In order for this market to escape further declines, I think we would have to see the market begin to stabilize and not slip in and out of the plus and minus column consistently."

Energy shares fell with the slump in oil prices, with the S&P energy index .SPNY losing 1.2 percent on the day and down 20.1 percent from its June high, entering bear market territory.

DOLLAR RISES, CRUDE SINKS

The U.S. dollar index rose as the euro sank after soft data including below-forecast readings on euro zone industrial output and the ZEW indicator of German investor sentiment.

"Weak numbers in Germany are like looking at the foundation of a home and realizing there's some rotten wood," said Douglas Borthwick, managing director at Chapdelaine Foreign Exchange in New York, on the implications of the German data on the euro zone economy.

The dollar index, which measures the U.S. currency against a basket of others .DXY, gained 0.3 percent after falling as much as 1 percent on Monday.

The euro EUR= handed back almost all the previous day's rise against the greenback. It recently traded down 0.7 percent at $1.2661. The yen JPY= dipped 0.2 percent to 107.02 per dollar.

Gold retreated from four-week highs as the U.S. dollar strengthened and data showed inflation running far below targets in various European countries. Spot gold XAU= last traded near $1,232 an ounce, down 0.4 percent.

Copper CMCU3 gained 1.3 percent on confidence about the outlook for demand from top consumer China following its plans to step-up infrastructure projects.