Eric Spiegel, chief executive in the US for Siemens , the German engineering group, said the problem exposed weaknesses in education and training in the US. Siemens had been forced to use more than 30 recruiters and hire staff from other companies to find the workers it needed for its expansion plans, even amid an unemployment rate of 9.1 percent

“There’s a mismatch between the jobs that are available, at least in our portfolio, and the people that we see out there,” Mr Spiegel told the Financial Times. “There is a shortage (of workers with the right skills.)”

He said Siemens was having to invest in education and training to meet its staffing needs, including apprenticeship programmes of the kind it uses in Germany. (Slideshow: What workers get, country by country).

His comments, made before Tim Geithner, the Treasury secretary, visits a Siemens plant in Ohio on Monday, suggest better education and training could help reduce the persistently high US unemployment rate.

The US labour market does not in general show signs of tightness: average wage growth in the year to the first quarter of 2011 was just 2 percent. Volkswagen , the German carmaker, had 85,000 applicants for 2,000 jobs at its new plant on Chattanooga, Tennessee.

However, a recent survey from Manpower, the employment agency, found that 52 percent of leading US companies reported difficulties in recruiting essential staff, up from 14 percent in 2010.

In manufacturing in particular there is evidence of a mismatch between workforce skills and available jobs: while employment has fallen since January 2009, the number of available job openings has risen from 98,000 to 230,000.

Mr Spiegel’s concerns about skills are shared by many other US business leaders, and were reflected this month in the first recommendations from President Barack Obama’s advisory council on jobs and competitiveness.

Responding to those concerns, the administration this month launched a nationwide expansion of the Skills for America’s Future programme, offering training, workforce development and job placements to help people find jobs in industry.

The programme is being run with the Manufacturing Institute, the think-tank affiliated to the National Association of Manufacturers. Emily Derocco, the institute’s president, said: “There is very definitely a gap between those that are unemployed or underemployed, and the education and skills that manufacturers require today. The companies are leaner and heavily technology-intensive, and require more than a high school diploma.”

Jeff Joerres, chief executive of Manpower, said businesses were more selective while the recovery was still weak and uncertain: “Employers have a much more sophisticated definition of skill requirements. Workers need to be instantly productive, and that makes a higher bar.”

The Nobel prize-winning economist Peter Diamond of the Massachusetts Institute of Technology, who was this month forced to withdraw from seeking a seat on the US Federal Reserve board of governors after Republican opposition, has argued that it can be worthwhile to invest in more education and training regardless of the general condition of the economy.