WASHINGTON (Reuters) - The small arms maker Sig Sauer Inc has sought U.S. approval to sell millions of dollars' worth of automatic assault rifles to the armed services of Mexico in a deal that will help to modernize the country's military, people familiar with the situation said.

       The U.S. Congress was notified last week that the Mexican Navy and Naval Infantry are in line to purchase as much as $5.5 million worth of automatic rifles made by Sig Sauer.

       The deal could be controversial because in the past weapons sold to Mexican authorities have found their way into the hands of criminals. Mexico's drug war violence has largely been carried out with weapons from the United States, imported both legally and illegally.

       Weapons that contain some parts or intellectual property from the United States fall under U.S. export control rules, requiring approval.

       Sig Sauer and the Mexican embassy in Washington did not respond to requests for comment.

       Based in New Hampshire, privately held Sig Sauer Inc. is the largest member of L&O Holdings, a worldwide business group of firearms manufacturers that includes J.P. Sauer & Sohn and Blaser Gmbh in Germany.

       "We are restricted under Federal law and regulations from confirming the licensing status of U.S. companies or entities or speaking to specific details on individual defense trade export licensing cases," a State Department spokesperson said.

       There are two major ways foreign governments purchase arms from U.S. companies: direct commercial sales negotiated between a government and a company; and foreign military sales, in which a foreign government typically contacts a Department of Defense official at the U.S. embassy in their capital.

       Both require approval by the U.S. government.

       (Reporting by Patricia Zengerle and Mike Stone in Washington; Editing by Dan Grebler)