By Joanne Chiu

International markets fell, tracking a steep U.S. selloff, on concerns that a resurgence in coronavirus infections could hold back economic recovery.

However, U.S. stock futures rose and bond prices fell, suggesting the drawdown might not extend much further, and some market participants said a pullback had been overdue after the recent robust rally.

Indexes in Asia dropped sharply, before later paring some losses. As of early afternoon Friday Hong Kong time, South Korea's Kospi Composite and Australia's S&P/ASX 200 fell around 2%, while Hong Kong's Hang Seng retreated more than 1%. Japan's Nikkei 225 fell and the Shanghai Composite also pulled back.

E-mini S&P 500 futures gained more than 1%, suggesting the U.S. index could recoup some of the 5.9% loss it suffered Thursday.

Stocks have rallied dramatically from a trough in March, buoyed by aggressive stimulus from central banks and governments, and by hopes the global economy will rebound sharply as countries reopen without a major surge in coronavirus cases.

But signs of an uptick have damped investors' optimism. Some U.S. states that were largely spared during the early days of the Covid-19 pandemic are now seeing record hospitalizations.

Gabriel Chan, head of investment services for Hong Kong at BNP Paribas Wealth Management, said global equities had become richly valued, after central banks pumped huge sums into the financial system, and thanks to optimism over the pace of economic recovery.

"It's a correction that is way overdue," Mr. Chan said. He said the market rebound had been "too quick and too sharp," implying a V-shaped economic recovery, while in reality the return to normality was likely to be bumpy.

Ken Peng, head of Asia investment strategy at Citi Private Bank, said the stance of Federal Reserve and its counterparts represented a major support for markets.

"There's just too much cash sitting around for this to be a deep correction," he said. "The Fed and other major central banks have already made it very clear they're there to buy the bottom basically," he said. In addition, Mr. Peng said any resurgence in infections was unlikely to lead to the same widespread shutdowns seen before.

On Thursday, Treasury Secretary Steven Mnuchin said it was extremely unlikely that parts of the U.S. economy would need to shut down again.

In bond markets, the yield on the 10-year Treasury note rose to 0.697% on Friday in Hong Kong, according to Tradeweb, up from 0.651% on Thursday afternoon in U.S. trading. Bond yields rise as prices fall.

Oil prices fell further. Brent crude, the global oil benchmark, retreated 2.2% to $37.70 a barrel, after tumbling 7.6% in the previous session. West Texas Intermediate, the main U.S. crude gauge, fell 2.5% to $35.45 a barrel.

Write to Joanne Chiu at joanne.chiu@wsj.com