US stocks pared gains on Thursday after the administration official's comments.
The official told reporters the tariff proclamations will allow other countries to discuss with the administration "alternative ways" to address the national security threat caused by their steel and aluminium exports to the United States, the official said.
Asked whether these would include voluntary export restraints, the official did not provide specifics, saying only that the order could be "flexibly modified".
The tariff plan has angered US allies - including Canada, Mexico, Britain and members of the European Union - who argue their exports to the United States do not pose a threat to US national security.
Some, including the EU, have threatened retaliatory tariffs on US products such as bourbon whiskey and Harley-Davidson motorcycles.
"All countries will be welcome to discuss with the United States alternative ways to address the threatened impairment of the national security caused by their imports," the official said.
The exemptions for Canada and Mexico would start immediately with an unspecified duration.
Their continuation depends partly on progress in negotiations to modernise the North American Free Trade Agreement, the official said.
He added NAFTA was an important part of the US-Canada-Mexico security relationship.
But the official said with any alternative remedies, it was important to maintain the target for increasing steel and aluminium industry capacity utilisation, which could result in higher tariffs for other countries.
"If Canada and Mexico were to be excluded, we would perhaps maybe have to raise the tariffs on everybody else - and modestly I might add, modestly - to ensure that our steel and aluminium industries are defended," he said.
The "wonderfully flexible document" is designed to accommodate US security relationships with other countries and provide "ironclad" protections for the industry, he said.
Ryan heads GOP backlash
The top Republican in the US Congress, Paul Ryan, publicly denounced Mr Trump after the tariffs announcement.
"I disagree with this action and fear its unintended consequences," the speaker of the House said in a statement, while welcoming the temporary exemptions granted to Mexico and Canada.
"We will continue to urge the administration to narrow this policy so that it is focused only on those countries and practices that violate trade law."
The House speaker's condemnation was swiftly echoed by other top Republicans in Congress, who fear the tariffs could spark a trade war and hurt the US economy.
"Trade wars are not won, they are only lost," Arizona Senator Jeff Flake, who has been highly critical of the president in the past, said.
Mr Flake called the tariffs "a marriage of two lethal poisons to economic growth -- protectionism and uncertainty", and promised to draft legislation to nullify them.
Orrin Hatch, the Utah Republican who chairs the Senate Finance Committee and who has enjoyed a close relationship with Mr Trump, called the president's latest move policy "misguided".
"Simply put: This is a tax hike on American manufacturers, workers and consumers," Mr Hatch said on Twitter.
"It undermines the benefits that the new tax law provides and runs counter to our goal of advancing pro-growth trade policies that will keep America competitive in the 21st century global economy," he said.
Canada to continue pushback despite exemption
Canada will continue to push back on US steel and aluminum import tariffs, despite being granted an exemption along with Mexico, Foreign Affairs Minister Chrystia Freeland said Thursday.
At the same time, she rejected Mr Trump's linkage of the levies to ongoing continental free trade talks.
"Today is a step forward. There is more hard work to do," Freeland told a news conference.
"In recent days, we have worked energetically with our American counterparts to secure an exemption for Canada from these tariffs," she said.
"This work continues and it will continue until the prospect of these duties is fully and permanently lifted."
Senior Canadian officials including the prime minister made a flurry of calls Wednesday and Thursday to American lawmakers and White House officials, hoping to head off the levies.
Canada is the largest foreign supplier of steel and aluminum to the United States.
In her comments, Ms Freeland pilloried the US national security justification for the measure, saying: "That Canada could pose any kind of security threat to the United States is inconceivable."
She also called the steel and aluminum tariffs and the North American Free Trade Agreement negotiations "separate issues," but added that a NAFTA deal was "within reach."
Canadian, Mexican and US trade officials are scheduled to meet in Washington at the end of the month for the next round of NAFTA negotiations.
Britain critical of tariffs
Britain's trade minister Liam Fox on Thursday criticised the US President's announcement of duties on steel and aluminium imports to America, saying it was the "wrong way" to resolve trade disputes.
"We can deal multilaterally with the overproduction of steel but this is the wrong way to go about it," he told the live TV audience of a BBC current affairs show.
"Protectionism, tariffs never really work," he added.
Mr Fox argued it was "doubly absurd" to target Britain with steel tariffs on national security grounds when it only provided the US with one percent of its imports and made steel for the American military.
The British steel industry could be badly hit by the tariffs, with trade body UK Steel saying the tariffs could have a "profound and detrimental impact".
Britain is currently a member of the European Union and would be bound by US measures against the bloc and any retaliation it launches.
France 'regrets' Mr Trump's new tariffs
France "regrets" Mr Trump's announcement of duties on steel and aluminium imports to the United States, Economy Minister Bruno Le Maire said Thursday.
"There are only losers in a trade war. With our EU partners, we will assess consequences on our industries and agree appropriate response," he tweeted.
Last Friday, Mr Le Maire warned that any such measures by the US would be "unacceptable" and called for a "strong, coordinated, united response from the EU".
The French minister then warned that the tariffs would have "a major impact on the European economy and on French companies such as Vallourec, ArcelorMittal and Ugitech".
"There are certain countries which practice dumping and other subsidies which distort global trade," he said, in an indirect reference to China. "The American authorities know that perfectly well, and it is this that they should be addressing, not anything else."
The White House said Thursday that countries concerned by the new tariffs could speak to the US in order to negotiate possible exemptions.
"The EU is a close ally of the US and we continue to think that the EU must be exempted from these measures," said EU Commissioner for Trade Cecilia Malmstrom.
"I will demand more clarity on this issue in the days to come," she added.
- with AFP