(CNN) Senate Majority Leader Mitch McConnell finally broke his silence Tuesday and denounced President Donald Trump's threat to place controversial tariffs on imported aluminum and steel, saying he has "genuine concerns" that it could trigger a trade war.

The majority leader's first public comments on the issue -- which has dominated headlines since it was announced Thursday -- came on the heels of a torrent of unusually blunt criticism from other GOP leaders and top committee chairmen, who spoke out against the retaliatory trade move immediately after Trump announced it last Thursday and every day since.

"There is a lot of concern among Republican senators that this could sort of metastasize into a larger trade war," McConnell told reporters when asked at a news conference about the tariffs, which generally are considered against GOP free-trade orthodoxy. "Many of our members are discussing with the administration just how broad, how sweeping this might be, and there is a high level of concern about interfering with what appears to be an economy that is taking off."

McConnell also defended the North American Free Trade Agreement, which Trump has vowed to drastically change, saying it has been a "big winner" for his home state of Kentucky.

"I would just say from a Kentucky point of view, NAFTA has been a big winner," McConnell said. "We have benefited from it in every way. So I think the best way to characterize where most Republican senators are right now, including myself, is genuine concern that this not escalate into something much broader."

His staff wouldn't explain why he hadn't spoken out earlier but disputed the notion that he was late to engage in the debate. One aide suggested McConnell's weekly Tuesday news conference was his first opportunity to make his views known, even though the leader has many other forums available to him, including his nearly daily speech on the Senate floor, when he typically talks about matters before Congress and in the news.

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McConnell spent much of the past few days -- in the weekly leadership meeting and in Tuesday's closed-door policy lunch -- gathering views from the unsettled members of his conference. He also attempted to get more information on the tariff proposal, which White House officials acknowledge publicly -- and, sources say, repeatedly in private to concerned lawmakers and aides -- remains far from complete or fully fleshed out.

"There's merit to not jumping the gun on this proposal given the guy who sits in the Oval Office," one Republican senator told CNN on Tuesday, noting that Trump can shift and vacillate on policies "depending on the day or who he spoke to last." The senator also pointed to what he called "an active effort" by White House aides opposed to tariffs to work behind the scenes to move the President off his position, one lawmakers have joined in both public statements and in private.

McConnell's caution may stem in part from hope that in the end Trump won't carry out his threat and will find another way to resolve his concerns about unfair trade.

"I think we need to wait and see what the White House finally decides to do on this," the majority leader said.

McConnell has a reputation as a disciplined politician who may prefer quieter, backdoor efforts to change Trump's mind instead of engaging in an open spat with the President, famous for his Twitter tirades. The senator's aides wouldn't specify what he's been doing to counter Trump's efforts but suggested he's done more behind the scenes than has been visible publicly.