From The Economist | The threat to world trade:
The tariffs are based on a little-used law that lets a president protect industry on grounds of national security.
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Although it doesn’t seem to be on the Federal Register (yet), the Presidential Proclamation on Adjusting Imports of Steel into the United States issued on March 8, 2018 has been published on whitehouse.gov.
The relevant law cited in the proclamation is section 232 of the Trade Expansion Act of 1962, which is codified at 19 U.S.C. § 1862 and provides:
[A]fter receiving a report ... in which the Secretary finds that an article is being imported into the United States in such quantities or under such circumstances as to threaten to impair the national security, the President shall ... if the President concurs, determine the nature and duration of the action that, in the judgment of the President, must be taken to adjust the imports of the article and its derivatives so that such imports will not threaten to impair the national security.
The Department of Commerce published its 262-page report, ‘The Effects of Imports of Steel on the National Security,’ on January 11, 2018.