"The petition for a writ of certiorari before judgment is denied", the Supreme Court said in its order list regarding the case.
The industry group argued that a key part of the law under which Trump imposed the duties violates the US Constitution.
The justices declined to hear the American Institute for International Steel's appeal of a March ruling by the US Court of International Trade, which rejected the group's lawsuit.
In March 2018, Trump introduced 25 percent tariffs on steel imports and 10 percent tariffs on aluminium imports by invoking Section 232 of US trade law citing alleged national security concerns.
The United States and European Union have been locked in what appeared to be an escalating trade war after Trump imposed tariffs on steel and aluminium imported from the European Union, Canada and Mexico a year ago. The European Union retaliated by levying its own tariffs on over $3.2 billion worth of the US imports, saying that the US tariffs targeted over $7.4 billion worth of the EU exports. Both sides also threatened to impose reciprocal tariffs on automobiles, agricultural and high-tech goods.