"He is committed to having a very fair and reciprocal military and trade relationship", Trump said on Twitter, referring to Turnbull.
Trump, who cited a rarely invoked national security section of United States trade law as the legal basis for his decision, said he aims to protect the USA industries.
Malmström will meet U.S. Trade Representative Robert Lighthizer in Brussels on Saturday to discuss an exemption. Trump said Thursday that countries with a "security relationship" with the United States could ask to be excluded.
After meetings with US trade envoy Robert Lighthizer in Brussels, EU and Japanese trade officials said negotiations would need to continue. "We should prevent a trade war situation from excessive protectionism, in which the entire world harms each other", Trade Minister Paik Un-gyu told a meeting with steelmakers.
Lighthizer did not make any immediate comment after the meetings.
But she warned that if the issue can't be resolved bilaterally or through the World Trade Organization, then "we will have to protect our industry with rebalancing measures".
The EU is also maintaining a threat of counter-measures that would target USA imports ranging from maize to motorcycles, and may publish its list next week to allow industry and other interested parties to give their input.
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EU Commissioner Cecilia Malmstrom, who coordinates policy for the world's biggest trading bloc, said she shared United States of America concerns about overcapacity in the steel sector but did not believe in tariffs as a way to solve the problem.
It remains unclear how hard it would be for the European Union to win an exemption. But he exempted Canada and Mexico and held out the possibility of excluding other allies.
But EU leaders, most of whom are also North Atlantic Treaty Organisation allies, say the argument is illegitimate because even during crisis they could still be expected to be reliable sources of the materials.
The Commerce Department also may look into removing certain products from the brunt of the hefty tariffs, he said.
Ms Malmstrom said on Friday that she would seek clarity on the USA decision and was counting on an European Union exemption. "So we are stumbling into a war, and this of course would be a great danger to the worldwide economy", said German MP Norbert Röttgen.
"We are living in historic times of unraveling, " he said.
It comes as Prime Minister Malcolm Turnbull confirmed Australia will be exempt from the tariffs once Mr Trump signs an executive order, .