By Joe Wallace

U.S. stock futures fell Wednesday as pockets of coronavirus infections emerged in several states, adding to concerns about a second wave of cases around the world that could lead to renewed restrictions on business activity.

Futures tied to the S&P 500 dropped 1%, suggesting the benchmark index will open lower in New York. The stocks gauge has risen for six of the past eight trading days, boosted by indicators showing a rebound in economic activity after a steep downturn in the spring.

New coronavirus cases have jumped in several states, with Arizona, Texas and California reporting daily records of infections Tuesday. Texas Gov. Greg Abbott and Florida Gov. Ron DeSantis said they would step up enforcement of social-distancing guidelines. California Gov. Gavin Newsom said earlier this week that the surge in cases could force the state to implement stricter measures on businesses and social gatherings once again.

"If this does get worse and more endemic, they will have to lock down some of these states again," said Charles Hepworth, an investment director at GAM Holding. "The U.S. has pretty much the worst case fatality rate of any major developed economy."

European stocks dropped, with the Stoxx Europe 600 falling 1.8%. Germany's Health Minister Jens Spahn said the coronavirus remained a risk after the western state of North-Rhine Westphalia on Tuesday locked down two municipalities following an outbreak at a meatpacking plant. The country's stocks benchmark, the DAX, fell 2.3%.

Also weighing on stocks, the U.S. said it was considering imposing tariffs on $3.1 billion worth of products from the U.K., France, Germany and Spain. The warning, which targets products including olives and malt beer, came in a review of the long-running dispute over government subsidies to aircraft manufacturers.

"The tensions between the Europeans and the U.S. have been bubbling under the surface for quite some time," said Jane Foley, head of foreign-exchange strategy at Rabobank. "Anything that suggests there is going to be tension on trade is bad for the global economy."

The federal government's top infectious-disease expert, Dr. Anthony Fauci, on Tuesday described the spike of infections in states such as Florida, Texas and Arizona as " a disturbing surge." Federal health officials said they were looking ahead to fall, when cases are expected to increase.

Parts of South Korea and Australia have also recently reported a resurgence in coronavirus infections.

"They're struggling to keep this totally under control," said Paul Jackson, head of asset allocation at research at Invesco, pointing to Germany and South Korea. "What's been more troubling in recent weeks is that globally, the daily deaths have flattened and are now on an upward trend."

Investors' concerns about the rise in infections have in recent weeks been tempered by optimism about stimulus measures from central banks and major governments, reflected in the rally in most major stock markets.

Investors will get another opportunity to parse the health of the world economy when the International Monetary Fund publishes its outlook at 9 a.m. ET. Earlier this month, the World Bank forecast that the global economy will shrink around 5.2% in 2020, making the coronavirus recession one of the most severe economic downturns of the past 150 years.

Major Asian stock benchmarks posted a mixed bag of results by the close of trading. Hong Kong's Hang Seng Index slipped 0.5%, while India's major gauge shed 1.6%. South Korea's Kospi gained 1.4% after North Korea suspended military plans directed against Seoul.

Oil prices fell as traders awaited weekly data showing the size of U.S. petroleum stockpiles from the Energy Department, due at 10:30 a.m. West Texas Intermediate futures dropped 1.4% to $39.82 a barrel.

Write to Joe Wallace at Joe.Wallace@wsj.com