It comes after the Prime Minister’s de facto deputy, David Lidington, rebuked Mr Trump for threatening a trade battle with the European Union.
Following a phone call between Mrs May and the president on Sunday, a Downing Street spokeswoman said: “The Prime Minister raised our deep concern at the President’s forthcoming announcement on steel and aluminium tariffs, noting that multilateral action was the only way to resolve the problem of global overcapacity in all parties’ interests.”
It marks the latest of the pair’s clashes, following disagreements over Mr Trump’s retweeting of anti-Muslim videos posted by the far-right group Britain First, and his recognition of Jerusalem as the capital of Israel.
In a further escalation, Mr Trump has said the US “will simply apply a TAX” on cars made in Europe if the EU retaliates against the trade penalties he is seeking on imports of steel and aluminium.
Mr Lidington told BBC One’s Sunday Politics programme: “I just think that the United States is not taking an advisable course in threatening a trade war.
“Trade wars don’t do anybody any good.”
Brussels is promising retaliation against American exports if Mr Trump follows through on his idea, which he is warning he will do next week.
But the president responded, saying on Twitter: “If the EU wants to further increase their already massive tariffs and barriers on US companies doing business there, we will simply apply a Tax on their Cars which freely pour into the US. They make it impossible for our cars (and more) to sell there. Big trade imbalance!”
Mr Lidington suggested the American authorities could overrule any tariffs, as they did in the case of aircraft manufacturer Bombardier when Mr Trump’s administration threatened huge duties on its C-wing planes.
The minister said: “We’ll have to see what happens, I mean there was a lot of concerns recently about something comparable with regards aviation and the aircraft that were being produced in part by Bombardier in Belfast in Northern Ireland, and the American authorities at the end of the day struck that down, they said no that is not the way that we should be going.”
And he warned Mr Trump that Britain’s experience showed his plan would not work.
“We tried in Britain in the 60s and 70s protecting our car industry from competition,” Mr Lidington said.
“It actually didn’t work, it protected inefficiencies, we lost all our export markets because our competitors who were more competitive went out and gobbled those up from us, and the car industry had to go through a very, very painful restructuring to get to the success story it is now.”
Mrs May and Mr Trump also discussed the war in Syria.
“They discussed Syria, and the appalling humanitarian situation in Eastern Ghouta,” the spokeswoman said.
“They agreed it was a humanitarian catastrophe, and that the overwhelming responsibility for the heart-breaking human suffering lay with the Syrian regime and Russia, as the regime’s main backer.
“They agreed that Russia and others with influence over the Syrian regime must act now to cease their campaign of violence and to protect civilians.”