Germany on Thursday triggered the second stage of its three-step plan to deal with natural-gas shortages, moving closer to possible rationing this winter, which economists fear would deal a severe blow to manufacturers in Europe’s largest economy.

Data firm S&P Global said on Thursday that its U.S. composite purchasing managers index—which measures activity in both the manufacturing and services sectors—fell to 51.2 in June from 53.6 the previous month to reach a five-month low. In the eurozone, the index fell to 51.9 in June from 54.8 in May, a 16-month low. A reading above 50.0 points to an expansion in activity, while a figure below that threshold points to a contraction.

The surveys join other indicators that point to a slowing in the world’s largest economy as U.S. consumers and businesses face rising prices and higher interest rates. U.S. retail sales fell in May, the first decline this year; existing-home sales have declined in four consecutive months; the average 30-year fixed-rate mortgage rose to 5.81% in the week ending Thursday, the highest since 2008, according to Freddie Mac. The labor market has remained strong while showing signs of slowing.

Inflation running at a four-decade high and high gasoline prices have also put U.S. consumers in a sour mood. A measure of U.S. consumer sentiment produced by the University of Michigan recorded its lowest level ever this month.

The results point to a U.S. economy that will grow at an annualized rate of less than 1% in June and contract in the third quarter, said Chris Williamson, chief business economist at S&P Global. In Europe, survey readings point to a second-quarter growth rate of 0.2%, down from 0.6% in the first quarter, he said.

“Having enjoyed a miniboom from consumers returning after the relaxation of pandemic restrictions, many services firms are now seeing households increasingly struggle with the rising cost of living,” he said. “There has consequently been a remarkable drop in demand for goods and services during June compared to prior months.”

Manufacturing output in both the U.S. and Europe declined for the first time in two years, while a services sector that had been boosted over recent months by the lifting of Covid-19 restrictions cooled sharply, the surveys showed.

In Europe, June’s slowdown was the sharpest recorded since November 2008, at the peak of the global financial crisis, Mr. Williamson said.

While the composite

PMI

for the U.K. was unchanged in June, that was after a sharp decline in May that left the measure at a 15-month low.

Elements of the survey pointed to even tougher times ahead, with new orders for goods and services falling in the U.S. and flatlining in Europe for the first time since the beginning of the economy’s recovery from the pandemic.

While businesses continued to hire new workers, they did so at a slower pace. In some cases, firms said they weren’t replacing departing employees as demand has slowed.

At the same time, the surveys for Europe also indicated that the prices charged by businesses continued to rise sharply. U.S. prices also rose, but at a softer pace.

“With the price indices remaining extremely strong, the eurozone appears to have entered a period of stagflation,” said Jack Allen-Reynolds, an economist at Capital Economics, referring to a sustained period of stagnant growth paired with rising prices.

The Federal Reserve is in the process of rapidly raising interest rates in an effort to contain inflation. Officials raised interest rates by 0.75 percentage-point on June 15, the biggest increase since 1994, and suggested they would make a similar move in July. Fed Chairman

Jerome Powell

told lawmakers this week that the Fed’s fight against inflation could lead it to raise interest rates high enough to cause a recession.

“It’s not our intended outcome at all, but it’s certainly a possibility,” he said.

The global economy faces a series of obstacles this year, ranging from Covid-19 lockdowns in China to soaring energy and food prices, Russia’s invasion of Ukraine and a broadening drive by central banks to combat high inflation by increasing borrowing costs.

For many economists, the invasion of Ukraine has been the decisive factor, since it has sent energy costs surging and pushed food prices higher while inflation had already exceeded central-bank targets.

“The Russia-Ukraine war has fundamentally transformed the global economy’s trajectory and that of Europe in particular,” economists at

Barclays

wrote in their latest quarterly report on the global outlook.

The economists on Thursday cut their forecasts for global economic growth, and now see the U.S. economy growing by 2.2% this year and 1.1% in 2023, having previously projected expansions of 3.5% and 2.3% respectively.

For the eurozone, they now see the economy in recession in the final quarter of this year and the first quarter of next year, and expanding by just 0.5% in 2023, a year in which growth had previously been forecast at 2.1%.

Companies are bracing for a possible recession. At

Ford Motor Co.

, higher commodity costs are eating into profitability in some areas,

John Lawler,

the company’s chief financial officer, said at a conference last week. The company’s financing arm has noticed an uptick in auto loan delinquencies, he added.

In Germany, the government moved closer to rationing natural gas on Thursday and triggered the second of three steps in its plan to deal with shortages after the Kremlin-controlled energy company Gazprom, Russia’s biggest gas exporter, throttled deliveries via the Nordstream pipeline by around 60% last week.

Germany’s gas reserves are at 58% capacity, and the government now expects a gas shortage by December if supplies don’t pick up, Economy Minister

Robert Habeck

said. The step is a prerequisite for the government to enforce some of the gas-saving measures it announced at the weekend, including substituting coal for gas in power generation and creating financial incentives for companies to consume less gas.

Rationing, which would come in the third step, would focus on industry and could severely affect companies that use gas as fuel or as a raw material for production, likely pushing Europe’s biggest economy into recession, economists and company executives have warned.

—Bojan Pancevski and Georgi Kantchev contributed to this article.

Write to Paul Hannon at paul.hannon@wsj.com and David Harrison at david.harrison@wsj.com