By Friedrich Geiger

BERLIN—As the flow of asylum seekers entering Germany started to break historic records last fall, Continental AG rushed to tap some of the newcomers for its workforce.

But one year after the tire maker began advertising an internship program designed for 50 migrant workers, only 30 of the positions have been filled as it struggles to find suitable candidates or vet their qualifications.

Continental isn’t alone. Answering calls from Berlin to help in the country’s massive integration effort, German companies big and small have scouted refugee shelters and job centers for potential employees. Yet because of administrative bottlenecks and a mismatch in needed skills, the number of migrants in jobs with benefits was only about 25,000 higher in June than a year earlier, despite more than 736,000 arrivals in that time.

“It is a huge effort,” said Ariane Reinhart, Continental’s executive board member for human relations.

Frustrated with the slow pace of hiring, Chancellor Angela Merkel invited senior executives from the 121 companies behind a jobs-for-refugees initiative called “Us Together” to discuss their progress and difficulties on Wednesday.

More than 80 business leaders attended the three-hour meeting. Among those questioned by Ms. Merkel were top executives at Deutsche Bank AG and Lufthansa AG . “It is our common target to integrate more and more refugees into the labor market,” she said beforehand. “If we succeed, it will be a benefit for all.”

Afterward, an “Us Together” spokeswoman said there was “an open exchange” about existing projects.

Failure to integrate the recent arrivals into Germany’s economy, the largest in Europe, could seal Ms. Merkel’s political fate. The chancellor’s popularity has waned, and her party lost badly in recent regional elections as more Germans doubt the wisdom of opening the country’s doors, which has brought well over a million migrants into the country in the past 18 months. Ms. Merkel has until the general election next year to change their minds.

Companies blame the difficulty in hiring migrants on shortcomings in speaking German and lack of relevant skills, in part because many are young. They also say administrative and legal red tape forces many migrants to delay the job hunt until after their asylum claims are processed.

Deutsche Post AG offered internships for 1,000 refugees last year but has so far filled only 235 positions. A spokeswoman said the postal services company relies on employment agencies for help in finding interns. It employs 102 refugees, it said, many of them former interns.

Deutsche Lufthansa AG, the airline, said it had yet to hire any refugees, citing security reasons. Background checks on refugees aren’t “always easily doable against the backdrop of the often adventurous circumstances in the former home countries or during their flight,” a spokesman said.

The government isn’t faring much better: Federal agencies have hired five refugees as employees and 12 as trainees since the beginning of last year, the interior ministry told lawmakers last month.

This is despite the fact that there are few native Germans available to fill the highest number of job vacancies in a decade, and shortages of skilled workers are putting upward pressure on wages.

Mohammed Fdeilati, a 22-year-old Syrian, said he fled to Germany two years ago, after finishing school, and became eligible to work after a year.

“I wanted to do an apprenticeship to become a train driver at Deutsche Bahn, but they demanded a certain language level which I couldn’t meet,” he said. After searching for a job for two or three months, he found one as a bartender in Berlin.

The Confederation of German Employers’ Associations said the country should broaden its German language and professional training for migrants and lower legal hurdles for their employment. Adult refugees should be sent back to school, it said.

So far, only refugees whose asylum applications have been accepted are required to attend language classes. The confederations is urging that the regulation be extended to migrants whose prospects of receiving asylum are good. Migrants also need more help to find a course, it said.

Lack of education and professional experience, along with deficiencies in speaking German and the young age of many migrants, are big stumbling blocks. Three out of five refugees looking for jobs are only qualified to fill entry-level positions, according to the Federal Labor Agency. Only 14% could work as specialists and 3% as experts, it said.

The thicket of German labor laws is an obstacle, too. In some regions, employers with vacancies are required to search for a German applicant before hiring a migrant. Asylum seekers can work for temporary employment agencies only after a 15-month waiting period. Many companies are also unwilling to invest in training workers whose long-term residency prospects are uncertain.

Most migrants lack the skills a sophisticated economy demands. German employers are mainly interested in skilled staff: Only 19% of all vacancies are for workers without adequate professional experience and education. Some 65% require midlevel qualification and 16% a university degree.

There are bright spots, however. Out of about 9,000 refugees applying for vocational training this summer, nearly 6,000 were accepted.

Internships typically last several weeks and are unpaid. While the numbers remain small, some companies said they were pleased. At sportswear giant Adidas AG , 15 refugees have completed internships as part of a two-year integration program, and another 15 are set to enroll by the end of the year.

“We’d be delighted if our interns decided after their two-year integration courses to do a traineeship at our company,” said Adidas spokeswoman Katja Schreiber.