Global stocks were mixed Monday, with U.S. markets closed for the July 4 holiday and futures pointing to a muted trading session at the open Tuesday.

The pan-continental Stoxx Europe 600 edged 0.3% higher, while the U.K.’s FTSE 100 index gained 0.6%. In Asia, major indexes closed on a mixed note.

S&P 500 futures wavered between gains and losses, while Nasdaq-100 futures slid just over 0.1%. Major U.S. stock indexes notched record closing highs Friday after a monthly employment report confirmed that the U.S. economy continued to recover at a healthy clip.

Investors say stock markets globally could be more choppy in the coming weeks as fresh data offer indications about the pace of economic recovery. Money managers are also awaiting signals from policy makers world-wide on whether they will weigh tightening easy-money policies that have aided the global recovery.

“For global equities, we’re entering a volatile backdrop,” said Georgina Taylor, a multiasset fund manager at Invesco. “Any central bank decision is having such an impact globally because it gives a sense of how policy makers are reacting to the data.”

Fresh figures released Monday showed that activity in the eurozone’s manufacturing and services sectors continued to expand in June. Improving economic data and the expectation of consistent support from the European Central Bank have bolstered Ms. Taylor’s expectation that shares in the region could continue to perform well this year.

Among individual movers, shares of U.K. grocery chain WM Morrison Supermarkets jumped over 11% after Apollo Global Management said Monday it is considering a bid for the U.K. grocery chain. That is likely to trigger a potential three-way bidding war with Clayton, Dubilier & Rice and SoftBank Group Corp.’s Fortress Investment Group LLC. SoftBank shares fell 5.4% in Tokyo trading.

Brent crude, the global gauge of oil prices, rose 0.9% to $76.82 a barrel. The Organization of the Petroleum Exporting Countries and its Russia-led allies failed to reach a deal on boosting oil production Friday. Their meeting, originally slated to resume on Monday, was postponed.

Cryptocurrencies rose over the weekend, with bitcoin trading at $33,546.20 Monday, up 1.3% from its 5 p.m. ET level Friday. Ether, the second-largest cryptocurrency by market value, added more than 5% over the same period.

Hong Kong’s Hang Seng Index slid 0.6% by the close of trading on Monday.

Hong Kong’s Hang Seng Index slid 0.6% by the close of trading on Monday.

Photo: tyrone siu/Reuters

In Asia, Hong Kong’s Hang Seng Index and Japan’s Nikkei 225 both closed roughly 0.6% lower. Benchmarks in South Korea and Shanghai each added less than 0.5%.

Some of the biggest moves in the region were in Chinese tech stocks, with Hong Kong’s Hang Seng tech index retreating 2.3%. Shares in companies such as Tencent Holdings Ltd. , Alibaba Group Holding Ltd., and Meituan all dropped.

In recent days, Chinese regulators have launched a data-security review of ride-hailing giant Didi Global Inc. and told Chinese app stores to remove Didi’s app just days after Didi’s New York listing. On Monday, authorities announced probes of apps run by two other Chinese companies that recently listed in the U.S.

Such actions create short-term market disruption, said Kelvin Tay, regional chief investment officer at UBS Global Wealth Management in Singapore. “Investors cannot predict or forecast the regulatory actions, whereas they can forecast and predict earnings growth to a large degree of accuracy. This creates uncertainty,” he said.

Write to Chong Koh Ping at chong.kohping@wsj.com and Caitlin Ostroff at caitlin.ostroff@wsj.com