By Paul Hannon

Europe's economy bounced back strongly in July, according to fresh surveys, as households and businesses emerged from lockdowns to bolster hopes that the low levels of infection in the region could lay the groundwork for a recovery in the remainder of this year.

The strength of the rebound suggests that the global economy is set to expand in the three months through September, having contracted sharply in the second quarter as lockdowns stilled businesses around the world. However, new outbreaks and the fresh imposition of more localized restrictions make it uncertain exactly how rapidly activity will return to the levels seen before the pandemic.

Data firm IHS Markit said Friday its eurozone composite purchasing managers index -- a measure of manufacturing and service-sector activity -- surged to 54.8 from 48.5 in June, indicating that activity increased at the fastest pace in more than two years after four months of contraction. A level below 50.0 points to a decline in activity from the previous month, while a reading above that threshold points to an increase.

The results of similar surveys of the U.S. will be released later Friday, and are expected to point to a less rapid rebound from a less strict lockdown.

The increase in activity was stronger than economists had expected, in keeping with recent data that has pointed to a more rapid gain in household spending and manufacturing output than had been anticipated.

The strength of the rebound in part reflects the severity of the lockdowns imposed across Europe. France endured some of the strictest limits on movement and saw very large declines in its PMIs during lockdown, particularly in its services sector. In July, its composite PMI jumped to a 30-month high of 57.6, from 51.7 in June.

"What we found [in Europe] is that as the outlets start to open, the business starts to flourish again," said Coca-Cola Chief Executive James Quincey this week. "We are social creatures as humans and we like experiences. People will want to go out. There will be habits that will have changed, but we will go out and experience the world."

Staffing giant Randstad Holding NV on Tuesday reported a 25% fall in second-quarter revenue, but said that momentum had improved in recent weeks across its European operations, a contrast with the U.S.

"It's been gradual, up and down, open and close," Chief Executive Jacques van den Broek said of the U.S.'s recovery. "It's definitely not getting worse but it's not like the steeper thing that we see in Europe."

However, it is unclear whether the pace of the initial bounce back can be sustained, given the losses incurred by businesses during the lockdowns, and worries about a resurgence in the virus later in the year.

One worrying sign from the surveys was that businesses continued to fire workers, an indication that they aren't convinced the return to pre-pandemic activity will be rapid.

"The concern is that the recovery could falter after this initial revival," said IHS Markit chief business economist Chris Williamson. "Firms continue to reduce head counts to a worrying degree, with many worried that underlying demand is insufficient to sustain the recent improvement in output."

The surveys indicated that while businesses reported a pickup in new orders, those from overseas customers were still falling. Travel and tourism, which play a big role in the economies of Southern Europe, also remain subdued as restrictions remain in place on who can visit the continent.

"We work a lot with tourists and only a few Europeans have come back so far," said Rita Indaco, co-owner of wine bar and restaurant Masto in Rome, who said she was 60% to 70% under her normal level of business. "But there are no Americans, which for us were very important, and other nationalities such as the Australians."

Spain is currently Europe's largest market for air travel, but traffic is down 32% from January's pre-pandemic levels. That compares with shortfalls of 10% in China and 44% in the U.S., according to consulting firm OAG.

As in the U.S., some cities have been put back into lockdown as infections have risen, including Barcelona. That potential fate worries many business owners in Europe.

"People are scared about the future," said Stefania Del Poeta, owner of a homeware shop in Rome's Testaccio market. "They fear there will be another lockdown. And it will be terrible if it happens."

There are signs that consumers are troubled by the twin threats of infection and unemployment. A survey by the European Commission released Thursday showed consumer confidence fell in July, leaving sentiment well below its pre-pandemic levels.

"The path of recovery crucially depends on the fear of infection," said Jonathan Haskel, an interest-rate setter at the Bank of England. "It also depends on the fear, or realization, of unemployment."

Giovanni Legorano in Rome contributed to this article.

Write to Paul Hannon at paul.hannon@wsj.com