In its annual report on the jobs market, the Paris-based policy advisory body said wages have been rising faster than prices over the past year, but real wages remain below their late 2019 levels in a number of countries, including the U.S.

The OECD said there are signs that the jobs market is cooling, with the number of vacancies falling relative to the number of people looking for work. But it doesn’t expect to see the sharp rise in jobless rates that have accompanied past periods in which central banks have raised their key interest rates to cool inflation.

“The labor market remains pretty strong,” said Stefano Scarpetta, the OECD’s director for employment. “The labor market is easing, but slowly.”

In the U.S., the OECD expects employment to increase by less than 1% in both 2024 and 2025, with the unemployment rate remaining around 4%. That is broadly in line with the outlook across the OECD’s 38 members, which are mostly rich countries. The OECD forecast that employment will grow by 0.7% this year and next, having increased by 1.7% in 2023.

Workers suffered a decline in their real wages during the surge in consumer prices that began in early 2021. The OECD said that over the year through the first quarter of 2024, real wages were rising again as inflation cooled. Out of the 35 countries for which data was available, 29 recorded a rise in real wage. Among those that didn’t were France and Japan.

On average, real wages were 3.5% higher than a year earlier, a development that should support consumer spending and economic growth. However, real wages were still below their 2019 levels in 16 countries, including the U.S., where the shortfall stood at 0.8%.

The OECD expects the recovery in real wages to continue this year. Offsetting that upward pressure on prices, profit growth has slowed in most countries. While profits grew much more rapidly than wages in 2021, the OECD estimates that since the start of 2022, labor costs grew more rapidly than profits in about two-thirds of the countries with data available.

In the OECD’s view, a squeeze on profits can allow for further wage rises without triggering a fresh pickup in inflation. That is an outcome that central banks have feared since the start of the inflation surge.

“There are no signs of a price-wage spiral,” the OECD said.

However, it warned that wage rises could yet have an impact on inflation.

“Looking ahead, it will continue to be important to strike a balance between allowing wages to make up some of the ground they have lost in terms of purchasing power and limiting further inflationary pressures,” the OECD said.

The recovery of the job market from the initial blow delivered by the spread of the Covid-19 virus has been particularly strong for workers in lower-wage parts of the economy, and for women, the OECD said. In 17 of the 33 countries with available data, traditionally lower-pay industries saw a faster rise in real wages between 2019 and 2023, while employment growth for women has outpaced that of men over the same period.

“Wages are performing better in the lower end than in the middle or high end,” Scarpetta said.

Looking ahead, the OECD said the transition to jobs that produce lower greenhouse gas emissions could have big regional impacts, with many of the new jobs that are created being in different locations to those which are lost. The OECD estimates that just 7% of employment is in what it describes as high-emission industries, but those who lose their jobs might face a lengthy period of lower earnings without retraining.

Write to Paul Hannon at paul.hannon@wsj.com