By Caitlin Ostroff and Joanne Chiu

Stocks ticked up in Europe and Asia Monday in a session with light trading volumes as markets in the U.S. and U.K. remained closed.

Futures tied to the S&P 500 climbed almost 1.2%, following a 3.2% gain in the gauge last week after some states eased coronavirus restrictions. The pan-continental Stoxx Europe 600 advanced 1.3%.

"Traders really don't know what outlook to take," said Ipek Ozkardeskaya, senior analyst at Swissquote Bank. "If we don't hear bad news on coronavirus -- like a second wave -- the recovery should continue."

There are some early signs that the U.S. economy is starting what's likely to be a slow and painful recovery, with air travel and hotel bookings edging upward. For the first time since the pandemic forced widespread U.S. business closures in March, conditions in parts of the economy aren't getting worse, and might even be improving.

Coronavirus-related deaths in the U.S. neared 100,000, prompting officials to urge caution as Americans venture outside over the holiday weekend. Authorities across the world remain on high alert for a second wave of infections -- which could trigger another round of lockdowns that further cripple the economy -- as restrictions are eased in many regions. The Trump administration imposed new travel restrictions on Brazil on Sunday after Covid-19 cases there rose sharply.

Among European equities, Bayer was one of the best performers. The stock rose 8.7% following a report that the German chemical company has made significant headway in settling lawsuits in the U.S. related to its Roundup weedkiller. Shares in Deutsche Lufthansa gained almost 5% following a report that the German government reached an agreement with the airline on state aid.

Most major Asia-Pacific equity benchmarks closed higher on Monday, with Japan's Nikkei 225 Index climbing 1.7% and the Australian gauge advancing 2.2%.

Some markets were buoyed by optimism over economic reopening, aided by encouraging signs in indicators such as mobility and restaurant-booking data, according to Kerry Craig, global market strategist at J.P. Morgan Asset Management.

However, there are reasons for caution, including uncertainty about the pace of normalization, the potential for further cuts to corporate profit forecasts, and rising tension between China and trading partners including the U.S. and Australia, he said.

Traders are also paying close attention to renewed tensions between the U.S. and China, especially over Hong Kong. On Sunday, riot police fired tear gas and water cannons as protesters in Hong Kong defied social-distancing rules to return to the streets and vent anger at Beijing's plan to swiftly impose national-security laws over the city. The Hang Seng Index, which on Friday logged its worst day since July 2015, ended Monday up 0.1%.

There are renewed concerns about possible retreats by international businesses from Hong Kong, given worries about issues such as safety and freedom of speech, according to Stephen Innes, chief global markets strategist at AxiCorp.

"Are we going to get more exodus of foreign employees and possibly companies leaving Hong Kong? That's quite a concern," Mr. Innes said. He said Beijing's initiative could also stoke further U.S. criticism ahead of this fall's presidential election. "I think this just gives [President] Trump more fodder to grandstand," he said.

The Shanghai Composite Index was also little changed, after declining 1.9% on Friday. Chinese Foreign Minister Wang Yi on Sunday called for more cooperation with the U.S., saying American politicians he didn't name "have taken U.S.-China relations hostage and are pushing our two countries to the brink of a new Cold War."

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com and Joanne Chiu at joanne.chiu@wsj.com