Mr Fox says he will travel to Washington next week when he will discuss the new duties.
He said: "We will, of course, be looking to see how we can maximise the UK's case for exemption under these particular circumstances."
Steel imports will carry a 25% tariff while aluminium will have a 10% duty.
UK Steel says 7% of its steel exports go to the US, worth £360m.
The European Union says it will be asking for an exemption to the tariffs, a move that includes all 28 countries, including, of course, the UK.
President Trump claims that the US has suffered from "unfair trade" and that the tariffs will boost the domestic market.
Mr Fox said: "We understand the anxieties about steel over-production that the United States has but we believe there are other ways to tackle that on a multilateral basis."
Mr Trump's decision, which comes into effect in two weeks' time, has provoked widespread condemnation from the likes of China and France.
A spokesman for steelmaker ArcelorMittal said the industry faced a number of problems: "The steel industry has been characterised in recent years by overcapacity, high levels of imports and unfair trade.
"We have appreciated the efforts made by governments to address unfair imports in support of a level playing field. Fundamentally a solution must be found to address the high level of overcapacity that still exists. This is particularly important given steel's globally traded nature."