Tiffany Hsu / Los Angeles Times

LOS ANGELES — Though American employers advertised slightly more job openings in May, economists continued to predict high unemployment through 2013.

A total of 3.6 million available positions were posted last month — up about 200,000 from April and the second-highest level in nearly four years, according to the Bureau of Labor Statistics.

With 12.7 million people unemployed in May, that’s more than three job-seekers for each open spot.

The government report, known as JOLTS, showed more open jobs in the manufacturing and government sectors. But there were also more layoffs and discharges from the previous month — an increase of 142,000 to 1.9 million in May.

The labor market saw a net employment gain of 1.8 million jobs over the 12 months ending in May, with 5.1 million hires and 49.3 million so-called separations. Last week, the government said the jobless rate remained stuck at 8.2 percent in June.

That’s far below its recessionary peak of near 10 percent, according to a Tuesday report from the Organization for Economic Cooperation and Development.

Economists predict that U.S. unemployment will steadily drop through the fourth quarter of next year, eventually reaching 7.4 percent.

But nearly 1 in 3 unemployed workers in the U.S. has been jobless for at least a year. And resources to help job-seekers have been halved, according to the OECD report.

And across the 34 countries covered by the OECD, unemployment is expected to remain high at 7.7 percent through the end of 2013, leaving 48-million people out of work — many of them young or low-skilled.

In the eurozone, joblessness is at an all-time high of 11.1 percent — reaching 24.6 percent in Spain. Unemployment is also in double digits in Estonia, France, Greece, Hungary, Ireland, Italy, Portugal and Slovakia.

In developed countries, many companies are reluctant to hire workers permanently because of the unstable economy, according to the report. The number of people out of work for two years or more has tripled since 2007 to 7.8 million, putting them at “a high risk of poverty and social exclusion.”