The US President set import tariffs on Thursday of 25 percent on steel and 10 percent on aluminium, to come into force in 15 days.
But he exempted Canada and Mexico and held out the possibility of excluding other allies.
EU and Japanese officials are now pushing for them to be included in the exclusions.
But, after meetings with US trade envoy Robert Lighthizer in Brussels today, trade officials said there had been no progress and negotiations would need to continue.
Donald Trump hit out again on Twitter afterwards, writing: “The European Union, wonderful countries who treat the US very badly on trade, are complaining about the tariffs on Steel & Aluminum.
“If they drop their horrific barriers & tariffs on US products going in, we will likewise drop ours. Big Deficit. If not, we Tax Cars etc. FAIR!”
Europe’s trade chief Cecilia Malmstrom described talks with Mr Lighthizer as “frank” and said they had not brought clarity on the exemption procedure. Talks would continue next week.
She said: ”As a close security and trade partner of the US, the EU must be excluded from the announced measures.
Japanese Trade Minister Hiroshige Seko said he had expressed his country’s concern to Mr Lighthizer and warned of major market disruption.
He said: ”We call for calm-headed behaviour.”
European Commission Vice President Jyrki Katainen warned Washington on Friday not to expect any concessions to win an exemption.
He said: ”This is not a trade negotiation.
“We are talking about unilateral action against international rules.”
The European Commission, which coordinates trade policy for the 28-nation EU, the world’s biggest trading bloc, has said it is ready to impose safeguards, tariffs or quotas to protect its own steel and aluminium industries from products diverted to Europe because of the US measures.
It has already started monitoring incoming metal flows to see whether a surge occurs.
It is also preparing countermeasures, including tariffs on US products such as cranberries, orange juice, whiskey, corn and peanut butter.