Washington (CNN) Conservatives -- including House Speaker Paul Ryan -- are striking back after President Donald Trump announced last week he planned to raise tariffs on aluminum and steel coming into the US.

"We are extremely worried about the consequences of a trade war and are urging the White House to not advance with this plan," Ryan spokeswoman AshLee Strong said in a statement Monday morning. "The new tax reform law has boosted the economy and we certainly don't want to jeopardize those gains."

Asked about Ryan's comments, Trump told reporters Monday, "No, we're not backing down."

Two GOP aides told CNN that leaders are not ruling out legislative action later on, but at this point the focus is on lobbying Trump to reconsider the move altogether, or to just focus on much narrower action.

Leaders of the House Ways & Means Committee have drafted a letter to Trump expressing concerns about "the prospect of broad, global tariffs on aluminum and steel imports," according to Lauren Aronson, spokeswoman for the committee Chairman Kevin Brady.

"As the two Chairmen have reinforced, the Administration and Congress must work together on trade policies that build off the momentum of the President's tax cuts, which is why any tariffs should be narrow, targeted, and focused on addressing unfairly traded products, without disrupting the flow of fairly traded products for American businesses and consumers," Aronson said in a statement.

"We think tailoring the tariffs strengthens the President's hand in a major way and makes sure that American manufacturer workers aren't caught up in unintended consequences of a broader tariff action by the President," House Ways and Means Chairman Kevin Brady told reporters Monday.

Earlier Monday, Ryan's office blasted out a CNBC article that linked a drop in the markets to Trump's planned levies on steel and aluminum.

"Stocks opened lower on Monday as investors mulled over potential US steel and aluminum tariffs," the lead sentence of the story stated. The article has since been updated to reflect the most recent movements in the stock market, but the move underscores just how frustrated conservatives are.

In recent days, the President's actions on trade have stunned the GOP in new ways . In the wake of the announcement, Republicans haven't been shy about their displeasure with the Trump administration's decision. Many lawmakers have issued strong rebukes of Trump's plans and outside conservative groups have also spoken out.

"The President has very strongly held views on trade policy. I disagree with them," Sen. Pat Toomey, a Republican from Pennsylvania, told CNN on Monday. "This is not going to have an effect whatsoever on Chinese steel or aluminum, for instance ... it's going to raise the cost of all the products that we use that consume steel."

On Monday, the Club for Growth, an outside conservative group, announced opposition to the planned tariffs.

"The idea of imposing steel or aluminum tariffs of any kind is an affront to economic freedom," Club for Growth President David McIntosh said in a statement. "First and foremost, it's bad for the American worker. For every steel worker job that might be saved because of a tariff, our country will lose even more American jobs in auto plants, construction, and so many other industries."

The second ranking Republican in the Senate described Trump's tariffs as "premature" and suggested the Senate's Finance Committee hold hearings on the issue.

"I think everyone is understandably concerned about what is going to happen next," Sen. John Cornyn, a Texas Republican, told CNN. "I guess the President is going to have to actually order the tariffs. I don't know how much it's going to be or how much impact that is going to have."

Holding hearings is up to Sen. Orrin Hatch, chairman of the Finance Committee. The Utah Republican told reporters on Monday evening, "we're thinking about it" when asked if hearings could come this week.

Sen. John Thune, a South Dakota Republican who's a member of GOP leadership, told reporters Monday night that Republicans are still looking at what legislative recourse they have to stop Trump's action on trade, but first they are trying to convince him not to go through with it.

"First and foremost there is going to be an attempt to try to convince the President that he's headed down the wrong track, and hopefully get him to a point where he'll reconsider that decision," Thune said.

He added, "I know there's a lot of fairly strong concerns that this could really put at risk and in jeopardy much of the economic progress that we've seen in the last year as a result of the rollback in regulations and tax reform and a lot of other things. The economy is in a good place."

Sen. Pat Roberts, the chairman of the Senate Agriculture Committee, told reporters last week that Trump's decision on tariffs was the wrong one.

"Every time you do this, you get a retaliation. And agriculture is the number one target. I think this is terribly counterproductive for the (agriculture) economy and I'm not very happy," the Kansas Republican said.

House Freedom Caucus Chairman Mark Meadows said there is "zero chance" Congress can pass legislation to reverse the President's move to impose new tariffs on steel and aluminum imports.

"I'm not optimistic that a legislative response will make it. We had a hard time repealing Obamacare," Meadows said.

Pressed if he would support a bill to change the policy, Meadows said he won't answer hypotheticals and said flatly, "It just is not going to happen. We are all smart people around here and there is zero chance that there is going to be a legislative fix that comes out of the House or Senate to address this issue."

Meadows said he's spoken to administration officials, who say the move is part of a tactic by the President to force trading partners to get fairer deals across the board on bilateral trade agreements.

Asked if he agreed with that approach by the White House, Meadows said, "I would have probably looked at more targeted tariffs on finished goods from specific countries, but I'm not the President."

But Meadows did say the House should hold hearings on the potential impact of the tariffs.