TOKYO—When Prime Minister Shinzo Abe visits the U.S. this week, he will act as salesman-in-chief by marketing Japan’s high-speed rail system.

With the support of the government, Japanese companies are vying for chances to join three fast-train projects under consideration in the U.S. The three would link Los Angeles and San Francisco; Dallas and Houston; and New York and Washington with high-speed systems.

Exporting Japan’s bullet-train system, known as the Shinkansen, is an important element of Mr. Abe’s strategy to revive his nation’s economy. Winning contracts in the U.S. would help bolster Japan’s bid to expand business in other markets, particularly in Asia’s developing nations, and compete with rivals from China and Europe.

When he visits California as part of a weeklong tour that began Sunday, Mr. Abe is expected to deliver a speech seeking to persuade the state’s leadership of the advantages of the Japanese system, including its strong safety record, reliability and the availability of inexpensive financing, Japanese officials say.

The state broke ground in January on a high-speed link between Los Angeles and San Francisco—a signature project of Gov. Jerry Brown, with an estimated cost of $68 billion. But it has yet to choose a train supplier. At 559 kilometers, the distance between the two cities is similar to that of the popular Tokyo-Osaka route in Japan. There, the bullet train runs every five to 10 minutes. The trip takes 2 ½ hours.