By Anna Hirtenstein

Global stock markets were mostly lower Tuesday as investors grew anxious that the recent rally has gone too far amid gloomy economic forecasts.

Futures tied to the S&P 500 fell 0.7%, suggesting a pullback when U.S. markets open. The stock index closed higher for the fifth straight day on Monday, while the tech-heavy Nasdaq hit a record.

The pan-continental Stoxx Europe 600 slipped 1% Tuesday after reaching its highest level in nearly a month.

"Some investors will be taking profit after yesterday's rally," said Sebastien Galy, a macro strategist at Nordea Asset Management. "There's been a real divergence between what the market believes and the reality of the economy."

The Organization for Economic Cooperation and Development said Tuesday that unemployment rates in the world's advanced economies will reach the highest level this year since the Great Depression.

The European Commission released its Summer Forecast report, which downgraded its expectations for the trade bloc's economy. It is now expecting a contraction of 8.3% for 2020, down from its earlier prediction of 7.4%. It also forecast less growth next year than previously thought, indicating a longer downturn.

"Expectations about a V-shaped recovery have taken a hit," said Michael Hewson, a chief markets analyst at brokerage CMC Markets. "This means there's going to be a longer bottom, it's going to take awhile for economic activity to pick back up off the floor. It'll be very stop-start when it comes to trying to recover normal levels of activity."

Data released on German industrial production showed a rebound in activity in May after the country eased its lockdown, but came in below consensus expectations. Activity was still at least 20% below levels seen in February. Germany's DAX stock index traded down as much as 1.3%, among the worst performing gauges in Europe.

It "shows how difficult the return to normality will be," said Carsten Brzeski, chief economist for the eurozone at ING. "After the lifting of the lockdown measures, businesses must have been more reluctant than consumers."

In Asia, the Shanghai Composite closed up 0.4%, continuing a rally on Monday that pushed the index to its highest point since 2018. Hong Kong's Hang Seng Index edged down 1.4% and Japan's Nikkei 225 slipped 0.4%.

In premarket trading, shares of Carnival fell 2.4% after it canceled a series of cruises planned for the fourth quarter of 2020 and beginning of next year due to the coronavirus and resulting delays at shipyards.

In European equities, Bayer declined 6% after it hit a snag in the resolution of a lawsuit about a pesticide that allegedly causes health problems such as cancer. The judge handling the case raised concerns on how future claims would be dealt with and Bayer said it will address this at the preliminary approval hearing on July 24.

The yield on 10-year Treasurys edged down to 0.667% from 0.683% on Monday, declining for the second day as some investors sought safety. The WSJ Dollar Index, which measures the dollar against a basket of currencies, rose 0.2%.

The Australian dollar weakened 0.5% against the greenback after the Reserve Bank of Australia kept its policy rate at 0.25%. The country's benchmark stock index S&P ASX 200 initially climbed 0.4% but ended the day flat after Melbourne, the second-largest city, was locked down again in response to a second wave of coronavirus cases.

Investors are keeping a close eye on Covid-19 infection rates.

"We are in a situation where the latest news from the U.S., Germany, parts of the U.K. and the Melbourne lockdown in Australia, it just acts as a reminder to investors that not everything is going to proceed on a smooth trajectory," said Peter Dixon, an economist at Commerzbank.

Crude oil prices slipped. Brent, the global benchmark, retreated 0.5% to $42.87 a barrel. West Texas Intermediate futures, the U.S. crude gauge, fell 0.7%.

Write to Anna Hirtenstein at anna.hirtenstein@wsj.com