WASHINGTON — Administration officials signaled Sunday that President Donald Trump is determined to impose punishing tariffs on imported steel and aluminum, brushing aside an outcry from foreign allies, U.S. manufacturers, Republican lawmakers and some advisers that he may ignite a damaging trade war.

Trump’s commerce secretary, Wilbur Ross, and White House trade adviser Peter Navarro, the apparent winners of an internal administration battle over the issue, said that they expect the president to follow up swiftly on his announcement Thursday that he would invoke a little-used legal provision to single-handedly impose duties of 25 percent on imported steel and 10 percent on aluminum.

“We expect probably by the end of the week it will be signed,” Navarro said on CBS’ “Face the Nation.”

Navarro and Ross each suggested that Trump was unlikely to exempt allied countries from the tariffs, despite national-security concerns raised by some of his advisers. The president has instead invoked national security as a reason to press ahead with the tariffs.

“As soon as he starts exempting countries (from the tariffs), he has to raise the tariff on everybody else,” Navarro said on “Fox News Sunday.” Making trade allowances for good friends, he contended, was impractical: “As soon as he exempts one country, his phone starts ringing from the heads of state of other countries.”

Ross, on ABC’s “This Week,” said he believed Trump was “talking about a fairly broad brush” in applying the tariffs. “I have not heard him describe particular exemptions yet,” he said.

The president, who often doubles down in the face of criticism, has seemingly been unmoved by allies’ warnings that they would be forced to retaliate. More admonitions came in Sunday, as the British Embassy reported that Prime Minister Theresa May spoke with Trump by phone and raised “deep concern” over the tariffs.

May told Trump that “multilateral action was the only way to resolve the problem of global overcapacity in all parties’ interests,” according to the British statement. The White House did not immediately offer its own account of the conversation between the two leaders, whose relations have suffered periodic strains despite the long-standing friendship between the United States and Britain.

Sen. Lindsey Graham, R-S.C., offered a blunt public message to Trump: “You’re making a huge mistake.”

On CBS, Graham said China — the tariffs’ ostensible target, to punish Beijing for metals dumping — would feel little economic impact because it accounts for only a very small share of steel and aluminum imported into the U.S. American allies including Canada, the European Union, Japan and South Korea are more significant exporters.

At the same time, Graham said, the Chinese leadership might take offense at the move, even as Trump is seeking Chinese help in reining in North Korea.

Trump has insisted that tariffs will not only help boost the aluminum and steel industry, but also generate more manufacturing jobs. That claim has been met with skepticism in the business community and by many analysts who predict a net job loss and damage to the overall U.S. and world economy.

Sen. Chris Murphy, D-Conn., said on ABC that a trade fight with Europe would be a “gift to Russia” because it would weaken important alliances.