Both powers, two of the biggest trade partners with the United States, have asked for exemptions from the tariffs.
The EU's top trade official Cecilia Malmstroem will meet US Trade Representative Robert Lighthizer in Brussels from 9:00 am (0800 GMT) along with Japanese Economy Minister Hiroshige Seko.
After the meeting, Malmstrom tweeted, "No immediate clarity on the exact USA procedure for exemption.so discussions will continue next week". Not fair or sustainable.
When asked whether he is concerned the tariff policy could spark a global trade war that hurts the USA economy, Mnuchin insisted that "we have to defend USA interests".
In one alleged example of haphazard policy-making, a report this week said the president raised the tariff rates for branding purposes, increasing them from the 24 and 7 per cent recommended by the Department of Commerce - because he wanted nice, round numbers.
With the nation still reeling from the massacre at a Parkland, Florida high school that left 17 dead last month, the president called video game makers on the carpet to address whether the simulated violence of their products have contributed to the rise of school shootings in the United States.
President Donald Trump met with leaders in the video game industry this week to discuss violence in video games and whether games could be having an influence on those who carry out mass shootings. Accordingly, there are additional customs taxes on the agenda that will affect EU's imports of steel, clothing, textiles and footwear, and certain industrial products from the US.More news: Australia Told to be 'Respectful' After David Warner-Quinton de Kock Row
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Trump imposed the tariffs despite pleas from friends and allies who warned the new measure could ignite a trade war. Tit-for-tat retaliatory measures don't profit any country.
Trump danced around the question of whether the tariff threat will be used to bully Canada and Mexico at the NAFTA bargaining table.
The EU insists that it is committed to open, global trade.
She also downplayed a link made by Trump between NAFTA and the metals tariffs, saying they were separate issues.
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.
NAFTZ and its members have been strong supporters of the NAFTA and believe it has been an important factor in making US manufacturing more globally competitive, supporting high-value-added employment in the United States, expanding export markets for USA products and services, promoting efficient supply and value chains, and improving standards of living. China is the world's largest producer of "met coal", but it consumes it all and buys more from overseas, including from the U.S. Australia is also a major exporter of metallurgical coal.