Canada and Mexico will be exempt from the tariffs while negotiations continue over the North America Free Trade Agreement (Nafta).
"Ideally, some of them will be dealt with in this 15-day process so that they don't hit those countries", Mnuchin said Friday, citing the legal time-frame for implementing the tariffs.
Flanked by a handful of steel and aluminum workers, some wearing coveralls and holding hard hats, Trump presented the move as a way to rebuild vital industries decimated by foreign competition. "It's really an assault on our country", he continued.
Some pundits and lawmakers fear the tariffs could set off a trade war with the European Union that could prove destructive to some US industries, as well as the nation's economic vitality.
The EU had already sounded a stern warning on Wednesday as it readied to lash back with US -targeted tariffs of its own on everything from steel to peanut butter, orange juice, cranberries, bourbon and denim jeans.
Government and companies are already lining up for a break. Automakers say the tariffs will not apply to finished products that use foreign steel.
But there was political criticism aplenty, especially from Trump's own Republican Party.
Sen. Ron Johnson of Wisconsin is asking Commerce Secretary Wilbur Ross to answer several questions about the move. France warned there would be no winners in a trade war. The Bulgarian said that her message to Mr. Trump was to make a "careful assessment before taking any further step".
If the entire cost were passed to consumers, which may not be possible, it could add about $300 to the price of the average vehicle, said Kristen Dziczek, director of Center for Automotive Research's Industry, Labor & Economics Group.
If a trade war erupts, which economics say is likely, it will depress the US economy, slowing growth, which will harm American workers and investors.
"Government ministers and Theresa May must back Britain's steelworkers and manufacturing communities by securing assurances from President Trump that they will not be caught up in a global tariff war between the USA and countries such as China".
Trump could then follow through with a threatened new tariff on European-made vehicles.
Trump declared during the White House ceremony. He urged companies to buy American steel and thus avoid import tariffs.
Malmstroem underlined that the European Union is committed to open, global trade, and also to working with Washington on what the European Union believes is the cause of the steel industry's problem - an oversupply on global markets.
Senate Minority Whip Dick Durbin said in a statement that he supports Trump's decision to "put China on notice", but criticized the tariffs as too broad. "That Canada could be seen as a threat to USA security is inconceivable, " she said. He added that NAFTA was an important part of the US-Canada-Mexico security relationship. The talks are expected to resume early next month.
On North Korea, Mr Turnbull said he agreed with Mr Trump that there must be no relenting on the economic pressure that brought North Korea to the negotiating table.