By Tommy Stubbington 

Global stock markets steadied on Tuesday after heavy declines, as Chinese shares bounced back from their lows in another roller coaster session ahead of a much anticipated Federal Reserve meeting.

In Europe, the Stoxx Europe 600 ended the session 1.1% higher, snapping a five-session losing streak. The index had fallen 2.2% on Monday as the biggest one-day fall in eight years in the Shanghai Composite Index spilled over into global markets.

In the U.S., the S&P 500 was around 0.7% higher and the Dow Jones Industrial Average close to 0.6% higher at the European stock market close.

Shanghai shares closed 1.7% lower after falling as much as 5% earlier in the session. Japan's Nikkei index closed down 0.1%.

The rout in China has fanned fears over slowing growth in the world's second-largest economy, stalling a rally in Europe that began after Greece and its creditors agreed to negotiate a new bailout. Investors are also looking ahead to Wednesday's statement from the Fed, after a two-day meeting that begins Tuesday, for clues on the timing of an interest rate rise that some expect as soon as September.

The combination of a potential escalation of the crisis in Greece with problems in China and an imminent Fed rate rise is a worrying one for investors, said Rabobank analyst Michael Every.

"We appear to still have all three issues on the horizon," he said.

Iain Stealey, a bond fund manager, at J.P. Morgan Asset Management, which has around $1.8 trillion in assets under market globally, said that emerging market bonds were particularly likely to come under pressure ahead of a Fed rate rise.

Talks to complete a bailout program between Greece and its creditors were also due to start Tuesday, nearly a week later than planned.

Still, many investors remain relatively sanguine about the turmoil in the Chinese stock market, betting that shares elsewhere are relatively insulated from the volatility there.

"It is a hard market to get your money into, so people's exposure is limited," said Guy Foster, head of portfolio strategy at wealth manager Brewin Dolphin, which oversees GBP26.2 billion ($40.6 billion) of assets.

Eric Lascelles, chief economist at RBC Global Asset Management, which has around $307 billion under management globally, said that Chinese policy makers' support should also not be underestimated.

"The Chinese government is taking truly extraordinary steps to support the market, and additional action seems likely," he said.

Moves in China stocks are a poor barometer for what's happening in the country's economy, which is of far greater concern to investors, he said.

In currency markets, the euro fell 0.4% against the dollar to $1.1048 after a sharp rise on Monday.

In commodities, oil prices stabilized near four-month lows after being hit by the Chinese selloff. Brent crude was 0.4% higher at $53.71 a barrel shortly after the European close.

Gold fell 0.2% to $1,094.60 a troy ounce.

Josie Cox contributed to this article

Write to Tommy Stubbington at tommy.stubbington@wsj.com