TOKYO — Two of the world’s largest manufacturers of the machinery used to produce semiconductors, Applied Materials of the United States and Tokyo Electron of Japan, on Monday dropped plans to merge after the Department of Justice said that combining their businesses would restrict competition.

The proposed $10 billion deal was announced in September 2013, but the companies had struggled to come up with a plan the American antitrust authorities would approve. It would have combined two of the three largest players in a sector crucial to the production of modern electronic devices, from smartphones to televisions.

Microchip factories are becoming increasingly large and costly to build, even as prices for the tiny chips they produce are steadily tumbling. Pressure on suppliers of chip-making machinery is intense, and the industry has consolidated into a clique of large, technically sophisticated groups.

By joining forces, Applied Materials and Tokyo Electron had hoped to streamline research and development operations and benefit from greater manufacturing scale. They had also planned to save tens of millions of dollars in taxes by incorporating the new company in the Netherlands.