During his opening remarks at a prime minister's questions session in the Danish parliament, Rasmussen criticised US president Donald Trump over the tariffs.
From Friday this week, tariffs of 25% are to be placed on steel and 10% on aluminium imported into the US, with exemptions for Canada and Mexico. Trump announced the decision earlier this month.
The PM censured Trump for his protectionist approach.
“Trump's decision to introduce tariffs on steel and aluminium is damaging and short-sighted.
“Free trade is not a zero-sum game. Measures like the one being taken now are going in the wrong direction,” Rasmussen said.
The PM stated his conviction that European countries should respond to the US decision.
“The EU is the most vocal supporter of free trade at this stage. So the EU must also respond in a balanced way,” he said.
Trump justified the decision to introduce the tariffs by citing national security and said the US was suffering from "unfair trade" and that the move would boost the country's industry.
But the US steel and aluminium industries are currently behind those of rival nations.
EU Commission president Jean-Claude Juncker has promised a response to the US move.
The union has so far been unsuccessful in its attempts to negotiate its own exemption to the tariffs.
But a list of American imports that could face tariffs in the EU is reported to have been drawn up.