Inside the White House, the debate has pitted hard-liners like Peter Navarro, the president’s trade adviser, and Commerce Secretary Wilbur Ross against more pro-trade voices, like Mr. Trump’s chief economic adviser, Gary D. Cohn, who argue that the measure could disrupt international alliances and global supply chains.

Republican lawmakers have criticized tariffs as undercutting the $1.5 trillion tax cut that they worked in lock step to pass last year, saying tariffs are essentially a tax increase that would slow economic growth. On Monday, they floated the idea of congressional action to try to block tariffs, should the president impose them.

Representative Kevin Brady, Republican of Texas and chairman of the House Ways and Means Committee, circulated a letter Monday expressing concern over the tariffs. Senator Dan Sullivan, Republican of Alaska, said he spent the weekend speaking with members of Congress and “senior administration officials” about his opposition to the president’s plan.

“As you know the administration is split itself,” Mr. Sullivan said from the annual CERAWeek energy conference in Houston, noting that details of the tariffs remain sparse.

Mr. Trump has heard all sides’ arguments, but his view has remained steadfast, one White House official said.

Still, the official said, the president is mindful enough of the arguments against potentially tanking the stock market that he has been somewhat open to a move to narrow the scope and effects of the tariffs while avoiding the perception that he was relenting. That would echo the approach the administration took to winding down the president’s promises on the Deferred Action for Childhood Arrivals, or DACA, program, which has protected young immigrants brought illegally to the United States as children.