Scrambling to head off what some GOP lawmakers fear would be economically counter-productive tariffs backed by President Donald Trump on imported steel and aluminum, House Speaker Paul Ryan on Tuesday publicly called on the White House to focus such trade duties on specific countries, not on all nations sending those products to the United States.

"I think the smarter way to go is to make it more surgical and more targeted," Speaker Ryan told reporters at a Tuesday news conference when asked about his differences with the President on trade.

"Clearly there is over capacity, dumping and trans-shipping of steel and aluminum by some countries, particularly China," Ryan added, acknowledging the need for some type of trade action by the Trump Administration, but making clear that it should not be applied to all.

The public appeal by the Speaker came as Republicans in Congress searched for a way to limit the President's push for new tariffs, concerned it could start a trade war by prompting a response from European nations, and then maybe another reply by the President.

“I’m against new tariffs," said Sen. Rand Paul (R-KY) during an interview on Fox News. "They’re simply a tax on the consumer."

"These tariffs are not a tax on foreign steel and aluminum producers, they are a tax on American citizens and business," said Sen. Orrin Hatch (R-UT) at a Senate hearing. "The proposed tariffs would blunt the benefits of tax reform for all Americans."

At a separate hearing, Treasury Secretary Steven Mnuchin indicated the tariffs would not apply to Canada, indicating the ongoing debate within the Trump Administration on the final details.

At this point, the appeals from GOP lawmakers - and from aides inside the White House - have not changed the President's mind; Mr. Trump said on Monday that he was not backing down, as officials reminded reporters and lawmakers alike that trade was one of the central issues in the 2016 campaign for President.

"We have a great relationship with Speaker Ryan," White House Press Secretary Sarah Huckabee Sanders said on Monday.

"But that doesn't mean we have to agree on everything."