There has been strong condemnation overseas and in the US.
The U.S.is still renegotiating the North American Free Trade Agreement (NAFTA) with Mexico and Canada.
White House National Trade Council Director Peter Navarro said national security is the primary reason behind ending the two-month exemption from USA steel and aluminum tariffs for Europe, Canada and Mexico.
Trudeau said the Trump move will hurt US interests.
He ominously recalled the pre-World War II period saying, "economic nationalism leads to war".
"The steel that doesn't go to the US has to go somewhere, and it won't just happen equally around the world", Gareth Stace, director of UK Steel, said.
"We would expect declining sales to result in auto-industry job losses ranging from 18,000 to 40,000 by the end of 2019", the Council said in a blog post in March.
EU, Canada and Mexico also draw up retaliatory measures to Washington's stinging steel and aluminium duties.
Brussels has previously threatened to slap tariffs on United States products including bourbon, motorcycles and blue jeans. Shares in both companies fell.
Japan says it has detected apparent Chinese ship breaking N. Korea sanctions
Trump's letter, the aides said, was created to pressure the North on the worldwide stage for appearing to have cold feet. Activist Kim Young-hwan speaks at a symposium on North Korean human rights in Seoul on May 31, 2018.
Ottawa will also challenge the tariffs under NAFTA and World Trade Organisation rules, she said.
"It's a sad day for worldwide trade", said the economy secretary today, describing the United States' announcement of metal tariffs against its trade partners as "completely incomprehensible".
The CBI warned the move would "damage prosperity on both sides of the Atlantic". "But we need to respond". We're at the front door of a trade war. He said he hoped negotiations would continue to find solutions to outstanding trade issues.
A tariff is a tax on foreign goods and Trump's 25% tariff on imported steel and 10% tariff on imported aluminum will mean a big cost increase on raw materials that are used to make everything from cars to houses to keychains. But most of the aluminum Boeing uses is domestically produced.
The US administration also launched a national security investigation last week into vehicle and truck imports, using the same 1962 law it has applied to curb incoming steel and aluminium.
The Associated Press reports that French President Emmanuel Marcon told Trump during a phone call that the new tariffs on steel and aluminum on European, Mexican and Canadian imports are "illegal" and a "mistake". Trump said they were needed to protect the United States from unfair competition.
"We want open markets, free markets but we have to convince the USA administration", Mr Altmaier told German television. After this announcement, more than 100 Republican members of Congress signed a letter criticizing the decision. However, later he granted an exemption to the European Union and other USA allies; that reprieve expires Friday.
"We regret that. We would much rather move together in partnership".
Dr Fox said he would speak to U.S. commerce secretary Wilbur Ross about the situation again on Monday.
The US tariffs have sparked warnings that they could destroy Europe's steel industry, where prices could drop by up to 40 percent.