By Anna Isaac and Xie Yu

U.S. stock futures wavered Monday amid concerns that escalating tensions between Washington and Beijing will further weigh on trade between the world's two largest economies.

Futures tied to the S&P 500 shifted between small gains and losses, following rises in European and Asian indexes.

Investors said sentiment was tempered after Bloomberg News reported Monday that China has ordered companies to temporarily halt imports of some U.S. farm goods including soybeans. Such a move could add to the friction between the two countries, and sour the prospects for existing and new trade agreements. A trade war between the two countries roiled markets for much of 2019, and ended only after both sides agreed to a phase-one deal and pledged to continue negotiations to address other hot-button issues.

Tensions between the two nations have climbed again in recent weeks with U.S. officials expressing anger over how China handled the coronavirus outbreak. President Trump on Friday opted to downgrade relations with Hong Kong, saying China's decision to impose a national security law was "absolutely smothering Hong Kong freedoms" and made it impossible for the U.S. to continue treating the city with a special status.

"If it is true China will buy less soybeans, it will increase the chances of escalation with the U.S.," said Seema Shah, chief strategist at Principal Global Investors. Such a move would suggest that "China is predicting the upcoming U.S. election means that President Trump's bark will be worse than his bite."

In bond markets, the yield on the 10-year U.S. Treasury ticked up to 0.659%, from 0.650% Friday.

Ahead of the opening bell in New York, drug maker Pfizer fell 6.3% in off-hours trading. The company's shares first dropped after market close on Friday, when it said that it would stop a potential breast cancer treatment.

In European stocks, gains on the Stoxx Europe 600 were led by Associated British Foods, owner of clothing retailer Primark. Its shares rose nearly 9% after it said it would be opening stores in coming weeks in response to loosening government lockdowns.

Investors largely seemed to discount the clashes between police and civilians in the U.S. as the worst civil unrest in decades erupted in American cities this weekend.

"Markets are assuming it won't last. We've seen this all before, going back to the civil protests in the 1960s," said Ian Shepherdson, chief economist at Pantheon Macroeconomics. "If cities go on to be closed down due to curfews and so on, then that would be disastrous for companies trying to reopen. Too soon to tell."

European stocks edged higher at the start of the week, with the pan-continental Stoxx Europe 600 climbing 0.8%.

In Asia, Hong Kong's benchmark stock index led the region's markets higher, signaling investors' relief that Mr. Trump had refrained from definitive steps targeting the city or mainland China. The city's Hang Seng Index surged 3.4%.

Mr. Trump said Friday that the decision to stop treating Hong Kong as semi autonomous from Beijing would affect issues such as extradition arrangements, trade in certain high-technology products, and advice to U.S. travelers, but he stopped short of announcing specific actions.

Mr. Trump's statement on Hong Kong wasn't perceived as overly negative, likely because it didn't contain concrete measures on the phase-one trade deal or on Hong Kong sanctions, said Martin Hennecke, Asia investment director with St. James's Place Wealth Management.

Hong Kong is to some extent benefiting from U.S.-China tensions, which has helped create strong demand for secondary listings from Chinese companies that are already listed in the U.S., Mr. Hennecke said.

Official and private gauges of China's factory activity on Monday showed manufacturing expanding as more factories reopened for work in May. The benchmark Shanghai Composite Index added 2.2% by the close of trading.

In South Korea, the Kospi rose 1.8%, while Japan's Nikkei 225 rose 0.8%.

Markets are boosted by relief that the U.S. hasn't taken tougher measures, which could potentially have devastated the Hong Kong economy and had wider regional effects, according to Alex Au, managing director at Alphalex Capital Management, a hedge fund based in Hong Kong.

"The short-term overhang is removed," Mr. Au said.

The results from two surveys of purchasing managers at U.S. manufacturers will be disclosed at 9:45 a.m. ET and at 10 a.m.

Write to Anna Isaac at anna.isaac@wsj.com and Xie Yu at Yu.Xie@wsj.com