The exemptions - on national security grounds - included Canada, Mexico, spokeswoman Sarah Sanders said.
Reports, however, suggested the apparent softening of the US stance would last for only 30 days.
US President Donald Trump has said steel products will face a 25% tariff, with 10% on aluminium goods. He is expected to sign the plan on Thursday.
Meanwhile, China threatened an "appropriate and necessary response" in any trade war with the US.
Foreign Minister Wang Yi said China and the US should strive to be partners rather than rivals.
The EU has proposed retaliatory measures against a number of US goods including bourbon and peanut butter.
Despite opposition at home and abroad, Ms Sanders said the US president would sign the measures in by the end of the week.
But she added: "There are potential carve-outs for Mexico and Canada based on national security, and possibly other countries as well based on that process. That would be [on] a case-by-case and country by country basis."
President Trump has previously suggested that planned tariffs for Canada and Mexico could be abandoned if a "new and fair" North American Free Trade Agreement (Nafta) is signed.
White House trade policy adviser Peter Navarro said on Wednesday that the tariffs would start in 15 to 30 days' time and there would be "a clause that does not impose these tariffs immediately on Canada and Mexico". Both countries knew the president was not "messing around in this", he added.
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