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* Futures down: Dow 0.54%, S&P 0.59%, Nasdaq 0.60%

June 4 (Reuters) - U.S. stock futures fell on Tuesday after weak manufacturing data raised new worries about the strength of the U.S. economy, even as markets awaited a slew of reports this week to gauge how much growth has slowed.

Stocks slipped on Monday after survey data showed U.S. factory activity had slowed more than expected in May and construction spending slipped in April, although the S&P 500 and the Nasdaq closed the session slightly higher.

"It was a day when the U.S. economic exceptionalism theme was called into question," Chris Weston, head of research at Pepperstone, said in a note.

Megacap stocks including Nvidia, Apple, Alphabet and Meta were down between 0.3% and 0.9% in premarket trading. Gains in these rate-sensitive stocks had boosted the Nasdaq in the previous session, as U.S. Treasury yields slipped.

Broadly strong corporate earnings, coupled with seemingly resilient economic growth, have kept Wall Street optimistic and buoyed stocks over several months, despite forcing markets to dial back hopes for both the timing and pace of interest-rate cuts.

However, a string of recent data points to the economy slowing more than expected, causing investors to fret even as markets expect an earlier start to rate cuts.

Traders are now pricing in a nearly 62% chance of the Fed cutting rates in September, up from about 53% before ISM data was released and under 50% last week, according to the CME's FedWatch tool.

Several key reports scheduled to be out this week are expected to provide a clearer picture of U.S. economic health, particularly the labor market. The Job Openings and Labor Turnover Survey is expected later on Tuesday, ahead of the closely watched nonfarm payroll figures for May, due on Friday.

Factory orders data is also expected later in the day and the results of surveys on the services sector are due on Wednesday.

"The manufacturing report has put us on notice that the various employment data points this week and ISM services could all be genuine market-moving risk events, and the market will likely be sensitive to any downside surprises," Weston said.

Monday's trading was also impacted by a glitch at the New York Stock Exchange, triggering volatility in dozens of stocks. The NYSE later said the issue had been resolved and exchanges were canceling erroneous trades in affected stocks, including Class A shares of Berkshire Hathaway.

At 5:51 a.m. ET, Dow e-minis were down 208 points, or 0.54%, S&P 500 e-minis were down 31.5 points, or 0.59%, and Nasdaq 100 e-minis were down 112 points, or 0.60%.

Among individual movers, Intel gained 2.3% after the company launched its next generation Xeon server processors, and priced its Gaudi 3 artificial intelligence accelerator chips below its rivals' products.

Software coding platform GitLab dipped 3.5% after forecasting weaker-than-expected second-quarter revenue late on Monday. (Reporting by Lisa Mattackal in Bengaluru; Editing by Pooja Desai)