Monday's US manufacturing data for May came in below expectations and indicated that a recent contraction is deepening, albeit slightly.

These figures follow other data that suggests the world's largest economy is slowing down in the face of the Federal Reserve's ongoing campaign of high interest rates as it battles to bring down elevated inflation.

Shortly after markets opened, the Dow Jones Industrial Average was trading down 0.2 percent at 38,487.50, and the broad-based S&P 500 slipped 0.3 percent to 5,270.89.

Meanwhile, the tech-rich Nasdaq Composite Index is down 0.2 percent at 16,790.70.

"Investors await more data that could elevate concerns about the health of the economy," Art Hogan from B Riley Wealth Management wrote in a note to clients before markets opened.

US Treasury yields appeared on track to continue recent declines, suggesting investors see interest rates coming down from their elevated levels in the not-too-distant future, as the economy slows down.

"Stocks are not responding favorably to the drop in Treasury yields," Briefing.com's Patrick O'Hare wrote in a note before markets opened on Tuesday.

This, he added, "suggests there is some budding angst that the drop in yields is an expression of concern that economic growth will be deteriorating and threatening earnings growth prospects."

Among individual stocks, the retailer Bath & Body Works was trading down 9.5 percent after providing underwhelming earnings guidance.

The US video game seller GameStop was trading down 4.5 percent a day after its shares popped on renewed enthusiasm for so-called "meme stocks" after a social media post by a popular trader known as "Roaring Kitty."

Investors are now looking ahead to Friday's payroll data, which will shed light on the health of the US labor market.