Senators are moving forward with legislation that would curb President Trump's authority on tariffs, despite opposition from the White House.

"If the president truly believes invoking Section 232 is necessary to protect the United States from a genuine threat, he should make the case to Congress and to the American people and do the hard work necessary to secure congressional approval," Sen. Bob Corker (R-Tenn.) said in a statement announcing the bill.

In addition to Corker, Sens. Heidi Heitkamp (D-N.D.), Pat Toomey (R-Pa.), Mark Warner (D-Va.), Lamar Alexander (R-Tenn.), Brian Schatz (D-Hawaii), Ron Johnson (R-Wis.), Chris Van Hollen (D-Md.), Mike Lee (R-Utah), Jeff Flake (R-Ariz.), Ben Sasse (R-Neb.) and Johnny Isakson (R-Ga.) are supporting the bill.

"There is no real national security threat that these tariffs are a response to. They are an effort to impose a protectionist policy for economic purposes," Toomey said in a floor speech blasting the administration's decisions.

The bill would require Trump to submit tariffs implemented under Section 232 of the trade law for approval to Congress. Any approval legislation would then be fast-tracked through both chambers.

Senators are introducing the legislation despite receiving pushback from Trump, who earlier on Wednesday privately urged Corker not to file his bill.

"I talked at length with the president about it today. He's obviously not pleased with this effort," Corker separately told reporters.

Corker added that Trump's main message in the phone call, which the president initiated, was for Corker to not move forward with the proposal.

But congressional Republicans are becoming increasingly frustrated with Trump's trade policy, which they worry could roil the economy just months before a midterm election.

The administration ratcheted up long-simmering tensions late last week when they announced that they would subject steel and aluminum imports from Canada, Mexico and the European Union to steep tariffs, ending an exemption for the trading allies.

A group of GOP senators met with Trump on Wednesday at the White House to discuss trade. The meeting was organized by GOP Sen. Lindsey Graham (S.C.).

"I think Sen. Graham, who is the leader of that meeting, just wants to talk to the president about his end game," Sen. John Cornyn (R-Texas) told reporters when asked about the meeting.

Graham said after the closed-door meeting that Trump is "on track to get us better trade deals" and signaled he will oppose Corker's legislation.

"Now is not the time to undercut President Trump's ability to negotiate better trade deals. I will not support any efforts that weaken his position," Graham said in a statement.

Notably missing from the supporters of Corker's bill are members of Senate GOP leadership.

Some GOP senators are wary of picking a fight with Trump, saying lawmakers should focus on trying to change the president's mind.

"I'm not sure right at this particular time it's advisable. ... My preference would be to convince the president that perhaps he should take a different approach," Sen. Pat Roberts (R-Kan.) told reporters.

Pressed if that strategy was working, Roberts acknowledged, "to date, no."

Sen. John Kennedy (R-La.) added that while he is reviewing Corker's legislation, he still believes "that the president is too smart to start a trade war."

Senate Majority Leader Mitch McConnell (R-Ky.) told reporters on Tuesday that he would not bring up the tariff legislation as a stand-alone bill but noted the National Defense Authorization Act (NDAA) was open to amendment.

"I'm not going to call it up free-standing. You're suggesting it might be offered as an amendment. NDAA's going to be opened, we'll see what amendments are offered," McConnell said, asked about Corker's bill.

Corker has pointed to the NDAA as one potential vehicle for his tariff legislation. But getting the bill brought up as an amendment to the defense policy bill would require the consent of every senator.

Sen. James Inhofe (R-Okla.), who is managing the bill in the absence of Armed Services Committee Chairman John McCain (R-Ariz.), said he thought Corker would ultimately be able to get a vote.

"I think it will. In fact, I told Corker that I would not object to it," Inhofe said, while noting he would vote against the amendment.

Asked if he thought Corker's bill should get a vote as part of the NDAA, Cornyn said the Senate should have an "open amendment process."

"It's the source of a lot of frustration here among members when people are denied an opportunity to vote. Back in the good old days ... we used to have [a] much more open amendment process," he said.

But the process for setting up roll call votes on amendments to the NDAA has ground to a halt in recent years as senators object to a vote on any amendment unless they can also get a vote on their own proposals.

Cornyn noted on Wednesday that there are already objections to amendments as lawmakers jockey for leverage, which could complicate Corker's quest to add his tariff legislation to the defense policy bill.

Business groups, considered a long-standing ally of Republicans, quickly backed Corker's bill.

Neil Bradley, the executive vice president and chief policy officer for the Chamber of Commerce, said on Wednesday that there was concern that Trump's tariff decision would cost American jobs.

"The constitutional authority of the Congress to 'regulate foreign trade' and its oversight of tariff policy is unambiguous. The modest proposal to clarify congressional prerogatives is welcome and long overdue," Bradley added.

There is no sign that the House is prepared to introduce similar legislation. Asked about the tariff legislation on Wednesday, Speaker Paul Ryan (Wis.) noted that Trump would have to sign the bill.

"You would have to pass a law that he would want to sign into law," he told reporters. "You can do the math on that."

Updated at 7:03 p.m.