By Saumya Vaishampayan And Alexandra Scaggs 

U.S. stocks inched lower Tuesday, a day after the Dow industrials posted their biggest one-day decline since early October.

Stocks in Europe stabilized, with the Stoxx Europe up 0.5%, even as other investments extended their moves from turbulent Monday trading. Oil prices continued to slide, and U.S. Treasury prices rallied further, pushing the yield on the 10-year note below 2%.

The Dow Jones Industrial Average dropped 13.68 points, or 0.8%, to 17487.97, and the S&P 500 slipped 1.84 points, or 0.09%, to 2018.74. The drop follows the steepest single-session drop for the Dow and S&P 500 since Oct. 9. The Nasdaq Composite Index slipped 15.77 points, or 0.34%, to 4636.8.

Early trading was choppy. Some investors were hesitant to buy amid lingering worries over the ongoing decline in oil prices and political instability in Europe, said Michael O'Rourke, chief market strategist at JonesTrading. Even with Tuesday's gains, the S&P 500 is down 1.6% in the first three trading days of the year.

"It was a rough start to the year," said Mr. O'Rourke. So now, "everyone is in this holding pattern."

Demand increased for assets considered to be havens on Tuesday. Treasurys gained, with the yield on the 10-year Treasury note falling to 1.990% from 2.038% on Monday. Yields fall as prices rise. Gold futures advanced 0.3% to $1208.10 an ounce.

Crude-oil futures continued to fall Tuesday, down 2.6% to $48.75 a barrel. Oil prices have tumbled more than 50% since mid-June.

Energy stocks stabilized in early trading, however. The sector was recently up less than 0.1%, after slumping 4% Monday.

While the decline in oil prices has led to lower gasoline prices and boosted the fortunes of consumers, it has also curbed profits for the once-booming energy sector, which has grown in recent years to become a bigger part of the U.S. economy.

"In the short term, it's stimulative for the economy and should be good for stocks," said John Brady, managing director at futures brokerage R.J. O'Brien, referring to lower oil prices. "It's almost like a tax cut."

"Longer term, there will be concerns about capital investment, especially in the oil and energy sectors, and you could see employment losses," which could be negative for stocks, he added.

Still, many investors expect stocks to gain this year, driven by an improving economy and rising corporate profits. Analysts expect companies will report 7.8% of earnings growth in 2015, according to FactSet.

Earnings reporting season for the fourth quarter of 2014 unofficially kicks off Jan. 12 with Alcoa Inc.'s report. Companies are expected to report 2.4% of earnings growth, according to FactSet, and 1.1% of sales growth from the previous year.

Tuesday's economic data was mixed. Service-sector activity grew at a slower pace than expected in December, according to the Institute for Supply Management. Its non-manufacturing purchasing managers' index slipped to 56.2 from 59.3 in November, while economists expected a reading of 58.0. But factory orders fell by less than expected in November, the Commerce Department reported, dropping 0.7% while a 0.8% decline was expected.

Asian stocks fell Tuesday, led by a 3% decline in Japan's Nikkei Stock Average. The commodity-sensitive Australian benchmark index lost 1.6%.

The Bank of Japan is likely to cut its price forecast again for the year ending in March because of the slump in global oil prices, The Wall Street Journal reported. Any cuts to its price projections could add to expectations for further policy action by the central bank.

In corporate news, Coach Inc. rose 0.4% after announcing it has agreed to acquire shoe brand Stuart Weitzman for $574 million. Coach will pay private-equity firm Sycamore Partners $530 million in cash and up to $44 million in contingent payments if it hits certain revenue targets over the next three years.

Write to Saumya Vaishampayan at saumya.vaishampayan@wsj.com and Alexandra Scaggs at alexandra.scaggs@wsj.com

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