By Joanne Chiu and Avantika Chilkoti

U.S. stock futures rallied Friday, reversing some of this week's selloff, as investors weighed data on the surge of the coronavirus in key states against government programs to shore up the economy.

S&P 500 stock futures gained almost 1%, suggesting the index could recoup some of the 5.9% loss it suffered Thursday.

In bond markets, the yield on the 10-year Treasury note rose to 0.689%, from 0.651% Thursday. Bond yields rise as prices fall.

International markets fell, tracking Thursday's U.S. selloff. In Europe, the Stoxx Europe 600 benchmark dipped 0.2%.

Indexes in Asia dropped sharply, before paring some losses. 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.

Figures released Friday showed the U.K. economy shrank by a fifth in April. The 20.4% decline provides the first detailed indication of the cost of the coronavirus-induced shutdowns on a major economy. U.S. gross domestic product figures for the second quarter are due to be published July 30.

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.

Oil prices fell further. Brent crude, the global oil benchmark, retreated 3.3% to $37.28 a barrel, after tumbling 7.6% in the previous session.

Write to Joanne Chiu at joanne.chiu@wsj.com and Avantika Chilkoti at Avantika.Chilkoti@wsj.com