The backlash against Donald Trump’s trade fight grew on Wednesday as steel users challenged the tariffs in court and carmakers warned of a surge in prices if the US president delivered on threats to extend them to more valuable auto imports.

In the most significant legal challenge to Mr Trump’s trade policies, the American Institute for International Steel said it had lodged an action in the US Court of International Trade to have the 1962 statute that the president used to impose steel tariffs ruled unconstitutional.

The president last year invoked a provision known as “Section 232” of the law to launch an investigation into whether steel and aluminium imports posed a threat to US national security. Last month he launched a similar probe into imports of cars and parts from worth more than $330 billion last year.

The challenge comes as pro-trade Republicans in Congress, backed by the US Chamber of Commerce and other business groups, seek to roll back the law and rein in the president’s ability to impose further tariffs. They have pointed to what they say is the potential economic damage and concerns of companies over escalating trade wars with China and the EU.

Automakers have said Mr Trump’s plans to impose tariffs on auto imports could raise prices of imported vehicles by as much as $6,000 per car and raise prices of locally made vehicles.

The Alliance of Automobile Manufacturers, which represents domestic and international car companies, has said that buyers of imported cars would face an average $5,800 price rise from a 25 per cent tariff.

“If this investigation leads to tariffs, retaliation against US exports is inevitable,” he said. “Substantial tariffs against major US auto exports have in fact already been announced, placing American auto workers on the front lines of this trade conflict,” he added, in an apparent reference to EU tariffs against Harley-Davidson motorcycles.

Ten of the 14 auto companies producing vehicles in the US today were based overseas, he said.

If other countries retaliate, job losses could climb to 624,000, the group said.