The international trade secretary told MPs he was “disappointed” with the US president’s decision to impose steel and aluminium tariffs on imports from the EU, which came into force on Friday.
US companies buying EU steel will now have to pay a 25% tax, while aluminium has a 10% tariff after Mr Trump cited national security interests.
The EU, Canada and Mexico had previously been granted exemptions after the announcement in March.
Speaking to the House of Commons on Monday Dr Fox said he hoped once the UK left the EU “we’ll have no problems with a UK exemption”.
Minutes before, the prime minister spoke to Mr Trump by phone, telling him the tariffs are “unjustified and deeply disappointing”, a spokesman said.
“They agreed to discuss this and wider issues of free and fair global trade further at the G7 summit later this week,” he added.
Dr Fox, who over the weekend called the tariffs “wrong and illegal”, warned on Monday the tariffs could lead to other countries following suit.
He welcomed the EU’s decision to take the matter to the World Trade Organisation (WTO), but said it could be difficult for it to act.
“The problem with using national security, as has been done in this case, is twofold,” he said.
“Were the United States to be successful, it sets a precedent for others to do the same and to use national security as pretext for protectionism, and secondly, it leads the WTO into the realms of having to determine what is and what is not acceptable as a definition for national security, something the WTO has always shied away from.”
The EU has decided to launch counter-tariffs on US products, including bourbon whiskey, jeans, Harley Davidson motorcycles and steel, starting from the end of June.
However Dr Fox refused to confirm whether the UK would back the counter-attack or not.
He said: “We still want to see what the measures themselves are, specifically we have been talking to the Irish government about the issue of bourbon being on the list because of the potential implications for the Scotch whisky industry and the Irish whiskey industry.”
Shadow international trade secretary Barry Gardiner urged the Government to “stand up” to Mr Trump.
“We do not want a trade war, most rational people believe there are no winners,” he said.
“Only President Trump has said he believes he can win one. The UK and the EU must stand up to this behaviour and restore the rules-based system.”
He called on ministers to raise the issue at this weekend’s G7 summit in Canada.
Gareth Stace, director of UK Steel, said the tariffs were a “hammer blow” to British producers.
“This cannot stand,” he said.
“Liam Fox has today shown that he stands with the UK steel sector in condemning the ‘unjustified’ US steel tariffs, supporting a strong and swift EU response, and using our close relationship with the US to exert influence where possible.
“The top priority for UK Government must be to continue to support the European Commission to secure a complete and permanent exemption for the EU from these absurd tariffs.”
And Labour MP John Mann suggested the UK should impose tariffs on overseas golf club owners in Scotland, where Mr Trump owns a course near Aberdeen.
Tory MP Jacob Rees-Mogg warned earlier that “tit-for-tat retaliation” could make a trade war worse, saying history shows “protectionism is worst for the country that imposes it”.