Trump "made clear that this would be an across-the-board tariff with no exclusions," the official told reporters.
However, the White House will consider possible exemptions in "situations" that arise on a case-by-case basis, the official said, speaking on condition of anonymity.
Refusing to spare friendly countries from the punishing tariffs could further inflame tensions created by Trump's sudden announcement on Thursday to protect American metal producers on national security grounds.
While Trump has long castigated China for unfair trade practices, the US, which is the world's largest importer of steel, buys most of it from allies like Canada, Brazil and South Korea.
Trump doubled down amid the firestorm on Friday, tweeting that "trade wars are good, and easy to win" and proposing "reciprocal taxes" on all goods from exporting countries which place duties on imports of US products.
The steel and aluminum announcement caught many in the administration and on Capitol Hill flat-footed. White House officials had not even completed a legal review of the proposed policies, sources told AFP.
Amid a global stocks selloff and irate reactions from trading partners and US industry groups, administration officials have moved to defend the policy, arguing that the tariffs would result in negligible price increases for durable goods and consumer items.
The White House official said the proposed 10 percent tariff on aluminum imports would result in a mere $25,000 increase in the price of a $330 million Boeing 777.
"There would be no unemployment that would result from this because we're in a tight labor market," the official said.
But economists cite the steel tariffs imposed in 2002 by then President George W. Bush, which resulted in hundreds of thousands of job losses and billions in lost wages before being rescinded after less than two years.
Industries that consume aluminum and steel products add far more to US economic output than companies which produce these metals.
"When you have the president of the United States going on the record and saying trade wars are good and they're easy to win, I shudder to think what that even means," Rufus Yerxa, president of the National Foreign Trade Council, told AFP.
Yerxa said the national security basis for the tariffs had never been applied to allies.
"This is a hostile act to all of them," he said. "This is saying you are a threat to our national security and that is about as outrageous as you can get."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)