Traders, already on edge owing to worries about rising interest rates, followed their US counterparts in heading to the hills after the president imposed levies on the commodities as part of his "America First" policy.
The news, which was even opposed by elements inside the White House, was met with anger from key allies including the EU and Canada. China has previously warned it would be forced to act should Trump push through such measures.
The tycoon had campaigned on a protectionist platform, saying the US was being taken advantage of by other countries, and promised to throw up barriers to protect jobs at home.
And analysts said there could be more to come.
"With the elevation of (trade hawk) Peter Navarro this week traders, markets, and business leaders are likely going to have to get used to these types of views continuing to shape policy," Greg McKenna, chief market strategist at AxiTrader, said in a note.
Navarro, a trade hawk and presidential aide, was by Trump's side as he made his remarks.
Wall Street's three main indexes ended sharply down for a third day, and those losses filtered through to Asia, where Tokyo ended 2.5 percent down while Hong Kong sank 1.5 percent and Seoul was one percent off.
Shanghai shed 0.6 percent, while Sydney and Singapore each gave up 0.8 percent.
Wellington, Manila, Taipei and Jakarta were also well down.