Sen. Orrin Hatch told reporters he didn't believe in tariffs and warned it could create more conflict for the US.
Speaking at a meeting with business executives at the White House, Trump also said he plans to impose a 10 percent tariff on imports of aluminum and keep the two measures in place indefinitely.
The administration has also cited national security interests for its action, saying the USS needs domestic supply for its tanks and warships.
The move also rattled global stock markets, with USA stocks selling off sharply and Japanese equities following suit in early Friday trade.
He also said worldwide trade was good for the economy - and that tariffs were "not the best approach" to protect American jobs. "And those people should be ashamed of themselves, what they've let happen".
Japan's Toyota Motor Corp said the tariffs would substantially raise costs and therefore prices of cars and trucks sold in America.
"I think it's a combination of the uncertainties that are becoming a little bit more apparent", said Maris Ogg, president at Tower Bridge Advisors.
The Dow Jones Industrial Average fell 420.22 points, or 1.68 per cent, to 24,608.98, the S&P 500 lost 36.16 points, or 1.33 per cent, to 2,677.67 and the Nasdaq Composite dropped 92.45 points, or 1.27 per cent, to 7,180.56.
"Should restrictions be imposed on Canadian steel and aluminium products, Canada will take responsive measures to defend its trade interests and workers", Foreign Minister Chrystia Freeland said in a statement, calling any trade restrictions "absolutely unacceptable". Imports make up about one-third of the 100 million tons of steel consumed by USA automakers, appliance manufacturers and other industries annually. Canada is the largest exporter of steel to the United States, as well as a major destination for USA steel exports.
Global trade lawyer Mark Warner said Canada could if it wished quickly apply tariffs on steel or aluminium or other targeted products. "If tariffs go up, it will, at the margin, tend to put more upward pressure on prices, and those upward pressure on prices will have to be considered by the monetary authority".
According to Farmers for Free Trade, a bipartisan group, previous trade spats with Canada and Mexico have triggered crippling tariffs on USA produce, dairy, pork, wine, beer and cheese. The Department of Commerce found that their quantities and circumstances "threaten to impair the national security". The Chinese probe is aimed at determining whether the U.S.is engaging in "dumping", or exporting the product at an unnaturally low price. That may hurt Trump in some farming states, where he enjoyed strong support in the 2016 election.
A spokeswoman for the Interstate Natural Gas Association of America said the tariff could pose a problem because the type of pipe and the steel used to make thick-walled interstate pipelines are not available off the shelf domestically.
It set off a chain reaction, with Canada, the European Union, and others vowing to retaliate.
"[Thursday's] ISM report is the latest signal that positive sentiment is giving way to euphoria in the manufacturing sector, yet this comes amid a run of admittedly lousy hard data", said John Silvia, chief economist at Wells Fargo.
A partially assembled Chevrolet 2017 Sonic is seen on the assembly line at GM's Orion Assembly plant in Orion, Michigan, U.S., June13, 2017. Risk "lies in the response of USA trading partners and whether the administration's decision to impose restrictive trade policies is only the first in a series of moves".
Trump reportedly faced opposition from within and outside his administration over the tariffs. The tariffs, he said, would remain for "a long period of time", but it was not immediately clear if certain trading partners would be exempt. Planning for the companies involved is easier.
Missouri Senator Roy Blunt said "My advice was.that you've gotta be careful here, you get into a tariff war". It previously called trade remedies for steel and aluminum long overdue.
Seko said Japan will communicate its stance to the United States while gathering more information about the proposed tariffs, Kyodo reported.
Contrary to the action announced by Mr Trump on Thursday, the Department of Defense had recommended targeted steel tariffs and a delay in aluminium duties. We want free, fair and SMART TRADE!