Stocks drifted lower on both sides of the Atlantic on Tuesday, while fresh measures to curb volatility prompted a rally in China.

In Europe, the Stoxx Europe 600 lost 0.4% as downbeat earnings hit shares. In the U.S., futures contracts showed the S&P 500 falling 0.2% at the open. Futures, however, don't always accurately reflect moves after the opening bell.

Stocks have slipped in recent sessions as falling oil prices weighed on energy shares. The Dow has lost 0.9% in the three trading days through Monday, and has fallen 3.9% from its all-time closing high in May. Declines in Apple Inc., which is a hefty component of the major stock indexes, have also added to the negative tone. And in the backdrop, investors continue to parse economic data for clues on when the Federal Reserve could begin raising rates for the first time in nearly a decade.

"There has been this notion for so many years now that you have to go in when the market pulls back," said Quincy Krosby, market strategist at Prudential Financial.

"You come in and buy on the dip because you've got a Fed that's going to be there for you. That is being questioned now," she added.

Economic data scheduled for release on Tuesday include factory orders. The focus shifts to labor-market reports later in the week, culminating with the government's employment report for July on Friday.

"If the Fed is in fact intent on liftoff in 2015, you need growth and demand for the market to go higher," said Ms. Krosby.

Oil prices rebounded on Tuesday after three straight sessions of losses, providing some relief for beaten-up U.S. energy stocks. Crude-oil futures rose 1.8% to $45.97 a barrel. Chevron Corp. and Exxon Mobil Corp. rose slightly in premarket trading.

The Shanghai Composite Index closed 3.7% higher after Chinese authorities late Monday moved to clamp down on short selling by implementing rules under which investors must wait at least one day to cover their positions and pay back loans used to buy shares.

When shorting a stock, investors sell borrowed shares in the belief they can buy them back at a much lower price later on, pocketing the difference.

Investors also kept a sharp eye on the main stock index in Athens on Tuesday, which fell 4.5% in early trade and was down 2.5% recently.

On Monday, the benchmark Athex Composite opened for the first time in just over five weeks and closed 16% lower, representing its biggest fall in percentage terms since at least January 1991, according to Thomson Reuters data.

In other markets, the euro was slightly higher against the dollar at $1.098. Gold futures added 0.2% to $1091.20 an ounce.

Treasury prices slipped, pushing the 10-year yield up to 2.170% from 2.150% on Monday.

Write to Saumya Vaishampayan at saumya.vaishampayan@wsj.com and Josie Cox at josie.cox@wsj.com

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