By Paul Hannon and Gwynn Guilford

China's services activity returned to strong growth in May after a three-month slump, while services in the U.S. and the rest of the world improved a little but continued to contract.

Services businesses, an important driver of growth in developed economies, were hit particularly hard by the coronavirus pandemic and related lockdowns. As shutdowns began to ease in May, surveys of purchasing managers showed that companies saw a pickup in activity for the first time since January but continued to cut jobs.

China's Caixin Purchasing Managers Index for the services sector rose to 55.0 in May from 44.4 in April, reaching its highest level for almost a decade. A reading above 50.0 points to an increase in activity, while a reading below that level points to a decline. China was the first major economy to begin reopening after the virus outbreak.

Results of surveys in the U.S. showed that the contraction in services activity continued in May, though at a lesser rate than in April.

The Institute for Supply Management's service index rose to 45.4 in May from 41.8 in April. Separately, private data firm IHS Markit said on Tuesday its U.S. services index climbed to a seasonally adjusted 37.5 in May, up from a record low of 26.7 the prior month.

Anthony Nieves, chair of ISM's services survey committee, said May's reading suggested a leveling off in the contraction that began in the second half of March, as the pandemic gained momentum. "All indications are that we're starting to bottom out and from there we'll see an upward growth pattern," he said. "The challenge is now with the unrest we have in the last week, that's put a damper on things," he added, referring to nationwide U.S. protests and some riots that followed the killing of George Floyd in Minneapolis while in police custody.

While three industries out of the 18 covered in ISM's survey saw a pickup in business activity in May, all but one reported reduced employment.

In Europe, job losses have been kept down by government programs that pay the wages of furloughed workers who are kept on by their employers. Figures released Wednesday showed that the number of unemployed people rose by 211,000 in April. During that same month, U.S. jobless numbers rose by almost 16 million.

The services surveys, combined with similar measures for manufacturing released Monday, suggest the global economy is set to contract even more sharply in the second quarter than it did in the first.

"This is the biggest recession we've experienced in our lifetime," said Jérôme Haegeli, chief economist at insurance company Swiss Re. "It's like a car crash, without an air bag."

Mr. Haegeli expects the global economy to contract by 3.9% this year, with the U.S. economy shrinking by 6.4% and China's economy growing by 2.7%. He expects the U.S. economy to grow by 4.2% in 2021, and 1.9% in 2022.

Elsewhere, purchasing managers' indexes pointed to continued contractions. India recorded the lowest PMI reading for services as lockdowns tightened in April. Its May reading rose only slightly, to 12.6 from 5.4. In Japan, the PMI rose to 26.5 from 21.5.

Across the eurozone as a whole, services activity weakened as governments began to lift the restrictions imposed in March and April. The currency area's PMI rose to 30.5 from 12.0.

"The downturn has already eased markedly in all countries surveyed," said Chris Williamson, chief economist at IHS Markit, the data firm that compiles the services surveys.

The prospects for recovery could be aided by European governments limiting unemployment. The European Union's statistics agency said the eurozone's jobless rate rose to 7.3% in April from 7.1% in March, a much smaller increase than expected by economists. Using the same method of calculation, the U.S. jobless rate stood at 14.7% in April, up from 4.4%.

According to the European Trade Union Institute, by the end of April businesses had applied for help to pay a quarter of the EU's workforce, or 42 million employees.

"The short-time work schemes absorb a lot of the immediate impact of the crisis on the labor market, but at the same time it also masks the job losses that are likely still up ahead," said Bert Colijn, an economist at ING Bank.

IHS Markit's survey for the U.S. registered broad-based job-cutting across the service sector in May. "The ongoing steep fall in employment remains a particular concern, pointing to a weakened consumer sector but also underscoring heightened risk aversion as companies seek to cut costs in the face of collapsing sales and an uncertain outlook," said Mr. Williamson, of IHS Markit.

In developed economies such as the U.S., services account for the bulk of economic activity. In the U.S., 80% of annual economic output is accounted for by services, compared with 69% in Germany and 53% in China, which relies more heavily on manufacturing.

Write to Paul Hannon at paul.hannon@wsj.com and Gwynn Guilford at gwynn.guilford@wsj.com