A visa program designed to supply skilled foreign workers to companies in the U.S. has slowed sharply, attracting about 50% fewer petitions so far this year than last year, and 80% fewer than in 2009.

Several factors have contributed to the decline in H-1B visas, including the lackluster pace of the U.S. recovery, more opportunities for skilled workers in their home nations and higher visa fees, which appear to have spurred Indian companies operating in the U.S. to seek fewer...