The Dow Jones Industrial Average dipped over one percent, S&P500 dropped 0.54 percent, while the Nasdaq was 0.16 percent in the red.
Ross said the USA would consider the effect of those measures.
President Trump had announced the tariffs in March, but gave several US allies temporary exemptions while they negotiated potential limits on shipments to the United States.
Meanwhile, Mexico has answered the U.S. tariffs with its own on products including pork bellies, grapes, apples and flat steel.
The United States used 5.5 million tonnes of aluminum previous year, largely imported from Canada, but only produced about 700,000 tonnes domestically.
"We in the United States are deeply concerned about the way the EU's new privacy guidelines, which came into effect last week, will force big changes in the way USA and European companies do business", Ross wrote in the Financial Times.
In late April, Trump delayed the tariffs until June 1 to allow space for trade negotiations, which proved fruitless.
The Mexican peso weakened by more than 1 percent against the dollar, briefly crossing the 20-to-the-dollar threshold to the weakest versus the greenback in 14 months.
"The numbers are clear: The United States has a $2 billion USA dollars surplus in steel trade with Canada - and Canada buys more American steel than any other country in the world, half of U.S. steel exports". They are the two-biggest suppliers of foreign vehicles to the U.S. In March, he said the U.S. would impose tariffs on imported steel and aluminium. Mexico said it would penalize USA imports including pork bellies, apples, grapes, cheeses and flat steel.
The Trump administration has given permanent metals tariff exemptions to several countries including Australia, Argentina and South Korea, but in each case set import quotas.
"Canada considers it frankly absurd that we would in any way be considered to be a national security threat to the United States", Freeland said.
Meanwhile, the commerce secretary said he plans to go to China for trade talks on Friday, another country with which the US has developed an extremely tense relationship over trade differences under the Trump administration. European officials argue that tit-for-tat tariffs will hurt growth on both sides of the Atlantic. "The Administration will continue to monitor steel and aluminum imports and adjust the measures in effect as necessary to protect the national security of the United States".
Ross explained that the previous extension for Canada and Mexico was specifically due to ongoing NAFTA talks, but that "those talks had been taking longer than we had hoped" and there's no longer a precise date of when a deal may be reached.
"We expect immediate retaliation from the European Union, which, on a net basis, to us serves no positive economic objective", KeyBanc analyst Philip Gibbs said in a note.