Trump said he is open to modifying tariffs for some countries - the Trump administration will allow any country that has a security relationship with the Trump administration to discuss potential modifications to "address the threatened impairment of the national security caused by imports from that country", the White House official added.
The tariffs were aimed at China, which has been dumping cheap, subsidized steel into the US and undercutting American producers who have been forced to slash production and jobs.
Robert Lighthizer, the United States trade envoy, will be leading negotiations with countries that want to be exempted from the tariffs.
The process of announcing the penalties has been the subject of an intense debate and chaotic exchanges within the White House, pitting hard-liners against free trade advocates such as outgoing economic adviser Gary Cohn aiming to add more flexibility for US trading partners. Republicans are concerned the imports could offset the benefits of the tax overhaul they worked too hard to pass previous year.
In addition to exemptions, there could be a consultation period that would lead to intense lobbying by industry and a growing group of disgruntled Republican lawmakers who oppose the tariffs proposed by the president, a fellow Republican.
While Trump claims the tariffs will help rein in China's unfair trading practices, Republicans like Sen.
Referring to a tweet by Tesla head Elan Musk, Trump said China charges 25 per cent duty on American cars whereas it is just 2.5 per cent on import of Chinese cars into the US.
Trump's chief economic advisor David Cohn also resigned on Tuesday in protest at the plans to introduce new tariffs.
In a statement in response to the exemption, Mexico's Economy Secretariat said that Mexico recognizes the problem of global steel oversupply, adding that "the negotiation process for the modernization of NAFTA is running its normal course".
In Tokyo, the steel industry was also concerned that the protectionist measures could affect global trade.
India's miniscule export of steel to the USA means it may breathe freely, but not other major countries.
European industry associations called on Malmstrom to respond if the EU was subjected to the tariffs, saying they would hit the steel and aluminium sectors hard.
"We urge the administration to take this risk seriously", Donohue said. A great country, a country long term partner will be doing something with them.