After September, the ECB said it expects a “gradual but sustained path of further increases in interest rates.” Unusually, the bank published its new staff inflation forecasts in its policy statement. They show eurozone inflation of 3.5% in 2023 and 2.1% in 2024, both above the ECB’s target rate.

“Inflation pressures have broadened and intensified, with prices for many goods and services increasing strongly,” the ECB said.

The ECB’s policy shift would come about a year after eurozone inflation rose above its 2% target. It would help to narrow the gap with the Federal Reserve, which has increased interest rates twice since March, to a range between 0.75% and 1%. Under the ECB’s plans, its key rate would rise to zero or higher after its Sept. 8 policy meeting, exiting negative territory for the first time in eight years.

The shift shows how the inflation problem across advanced economies looks increasingly similar to that of the U.S., even in places like Europe, where the economic recovery has been slower and government spending more restrained.

That partly reflects common global factors such as lockdowns in China and the war in Ukraine, which have driven up the costs of goods, food and commodities everywhere.

European stocks sold off after the announcement, with the Stoxx Europe 600 retreating 1.4%, while the euro rose 0.4% against the dollar. The yield on the benchmark 10-year Italian bond increased to 3.543%, the highest level since 2018. The equivalent German bund yield rose to the highest level since 2014 at 1.448%. Bond yields move inversely to prices.

Lee Hardman,

a currency analyst at MUFG, said the planned quarter-point increase was seen as more dovish than expected but the rest of the guidance appeared to send a more hawkish message. “The ECB is preparing the market for a more sustained period of rate hikes to get a grip on inflation risks,” he said.

But on both sides of the Atlantic, inflation is broadening beyond volatile energy and food prices to a range of goods and services, fanned by tight labor markets and easy money from central banks, economists say. The ECB, the Fed and other major central banks printed money on an unprecedented scale early in the pandemic to finance large-scale bond-buying programs aimed at stabilizing economic growth. Households accumulated a large amount of savings during the pandemic that are likely to be spent over time.

Core inflation—which strips out volatile food and energy prices, and is therefore considered a better predictor of future inflation—increased to 3.8% in the eurozone in May, by far the highest level since the common currency was launched in 1999. Core inflation has also risen to 4.1% in South Korea, 5.7% in Canada, and 6.2% in both the U.K. and the U.S. Most major central banks including the Fed and the ECB aim to keep inflation at 2% over time.

“The increase in core inflation across a number of advanced economies suggests that monetary policy has been too expansionary,” said Stefan Gerlach, former deputy governor of Ireland’s central bank.

Most studies say monetary policy’s impact on the economy takes about two years to play out, which suggests recent increases in inflation could have been triggered by central-bank stimulus early in the pandemic, Mr. Gerlach said.

Unlike the Fed and other central banks, the ECB drives monetary policy for a number of countries, which means it faces the delicate task of tightening monetary policy to battle inflation while trying not to weaken the bloc’s most fragile economies. This is why, unlike the Fed, it is expected to hold on to its mammoth portfolio of sovereign debt. The ECB’s balance sheet has almost doubled to about 8.8 trillion euros, equivalent to $9.39 trillion, since the start of the pandemic, swollen by large-scale bond purchases and cheap loans to households and firms.

Until recently, ECB President

Christine Lagarde

had said the ECB was very unlikely to raise interest rates at all this year, pointing to differences between the eurozone and U.S. economies, including slower wage growth in Europe. “Our economies do not compare,” Ms. Lagarde said in April.

Now, labor markets are relatively tight across Europe, wages are rising briskly in places like Germany and the Netherlands, and many countries are experiencing labor shortages. The eurozone’s unemployment rate has fallen to a record of 6.8%.

The prices of more products and services have risen sharply across advanced economies, a sign that high inflation could become entrenched. In the eurozone, the prices of around half the items in the inflation basket rose at annual rates above 4% over the year to April, according to the Organization for Economic Cooperation and Development, a Paris-based think tank. While even more of the U.S. basket is subject to inflation rates of 4% or more—about 60%—price growth has broadened significantly in both regions.

The OECD this week lowered its forecast for global growth this year by 1.5 percentage point to 3%, and warned that sharp interest-rate increases by central banks could slow growth further. Policy interest rates are expected to be around 2.5 percentage points higher in 2023 than in 2021 across its membership of mainly rich economies, the OECD said.

To be sure, core inflation is significantly higher in the U.S. than Europe, partly reflecting much larger government stimulus, which has powered consumer spending. The U.S. economy has moved above its precrisis growth path, while the eurozone still lags below it. U.S. wages have risen at an annualized rate of about 6%, roughly double the pace in the eurozone. Europe has a large number of job openings, but not nearly as many as the U.S. relative to the number of unemployed people.

Still, inflation on both sides of the Atlantic seems to be driven by strong demand as well as supply bottlenecks, a sign that it could persist.

“We consistently not only underestimated inflation, like in the U.S., we also consistently underestimated growth and the growth dynamics coming out of the pandemic. So there must also have been a demand element in the high inflation in Europe,” said

Klaas Knot,

who sits on the ECB’s rate-setting committee as governor of the Dutch central bank, at the World Economic Forum in Davos, Switzerland, last month.

Some ECB officials, including Mr. Knot, have suggested that the bank should increase its key interest rate by a half-point in July, echoing the aggressive path taken by the Fed. Investors are now pricing in five quarter-point ECB rate increases in total by year-end.

The Bank of England, the Bank of Canada and the Reserve Bank of Australia have also raised their main policy rates and started to reduce their bondholdings in recent months. In all three countries, unemployment is at multidecade or record lows. All three central banks conducted large-scale bond-purchase programs during the pandemic.

Some prominent economists have recently faulted major central banks for that strategy.

Mervyn King,

the former governor of the Bank of England, said last month that policy makers pumped too much money into the global economy at a time when many businesses were closed. Central banks now risk doing too little to return inflation to target, he said in an interview with Sky News.

“If you simply print lots of money at a time when you are producing less, you’ve got a classic case of too much money chasing too few goods and the result of that is inflation,” Mr. King said.

“It was a mistaken diagnosis,” he added. “They shouldn’t have been printing the extra money, what governments were doing was enough to deal with the consequences of Covid.”

—Anna Hirtenstein contributed to this article.

Write to Tom Fairless at tom.fairless@wsj.com