Global stocks were mixed Tuesday, as a recent slump in commodity prices continued to heap pressure on the oil sector, while fresh measures to curb volatility in China prompted a share rally there.

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.

In Europe, the Stoxx Europe 600 lost 0.5% in early trade.

The world's benchmark oil price fell to less than $50 a barrel on Monday for the first time in six months. Brent, the global benchmark, fell $2.69, or 5.2%, to $49.52 a barrel on ICE Futures Europe, representing the largest one-day loss since July 6 and the lowest settlement since Jan. 29.

Early on Tuesday in Europe, the price of Brent was 1% higher, hovering around the $50 mark.

The European subindex of oil and stocks fell 0.8%, and shares in exploration company Tullow Oil PLC, offshore drilling company Seadrill Ltd., Total SA and Statoil ASA, all fell by more than 1%.

The biggest gainer on the European index was German car manufacturer Continental AG. The group reported double-digit second quarter earnings on Tuesday, particularly citing growth in Asia.

Elsewhere in equity markets, investors will be keeping a sharp eye on the main stock index in Athens Tuesday, which opened for the first time in just over five weeks on Monday.

The benchmark Athex Composite slumped more than 22% on Monday before ending the day 16% lower, representing its biggest fall in percentage terms since at least January 1991, according to Thomson Reuters data. Early Tuesday the index was down 4.7%.

In currency markets, the euro was broadly flat against the dollar at $1.095. The dollar was also little changed against Japan's yen at ¥ 124.01.

Gold was 0.2% lower at $1,087.10 per troy ounce.

Write to Josie Cox at josie.cox@wsj.com

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