CEO Fred Smith, in separate media appearances on Tuesday, questioned Trump's decision to formally withdraw from the Trans-Pacific Partnership (TPP). The package and business services company employs thousands of people whose jobs depend on international trade.

"The United States being cut off from trade would be like trying to breathe without oxygen," Smith said in an interview with Fox Business Network's Maria Bartiromo.

Trump's protectionist tone boosted his popularity with white, working class voters during the election, who helped him win some traditionally Democratic areas even as his words put him at odds with Republican orthodoxy on free trade.

Smith on Tuesday argued that some 40 million Americans have jobs as a result of trade, whose benefits are more "diffuse" and harder to see than the "pain" in areas like manufacturing.

"It's an essential part of our economy. I think the decision to pull out of TPP is unfortunate because the real beneficiary of that is China. And China has been very mercantilist, very protectionist," Smith said.

"We need to try to stop those things and get the Chinese to open up their 1.3 billion person market, not cut them off. We have the opportunity to sell huge amounts of goods into China."

Smith's criticisms risk placing him in the president's crosshairs as Trump has shown a willingness to rip into companies or individuals who displease him.

"I wouldn't be surprised if Trump pushes back," said Republican strategist David Carney. "Trump's a new sheriff in town. The niceties of diplomacy and international trade... it's just not the Trump way."

Trump also risks friction with members of his own party who support free trade, said Republican strategist Tom Doherty.

On Monday, Trump signed an executive order to formally withdraw from the TPP as China's influence in the region grows. The Republican president has been critical of China, which was not a party to the TPP.

Trump also said he would renegotiate the North American Free Trade Agreement at an "appropriate time," following another campaign pledge to redo the NAFTA trade pact with Canada and Mexico.

Smith, who met with Trump in New York following his November election victory, urged the new president to reconsider his position toward the Asian powerhouse despite China's historic protectionism during an earlier interview on CBS' "This Morning."

"To some degree, the administration's positions are a little bit out of date with reality of China today. They want to open their markets today," Smith told CBS.

Since well before November's election, Smith, 72, criticized the positions of both Trump and Democratic rival Hillary Clinton, saying he hoped cooler heads would prevail after the election.

In June 2016, he told analysts on an earnings conference call, that anti-trade rhetoric and anti-business positions expressed on the campaign trail were "very worrisome."

FedEx, with revenues topping $50 billion last year, employs more than 400,000 people globally, according to its website.

Smith founded the global freight, package and business service company in 1971.

(Reporting by Susan Heavey; additional reporting by Luciana Lopez; Writing by Nick Zieminski; Editing by Jeffrey Benkoe and Alan Crosby)