(CNN) President Donald Trump's latest plan to lower drug prices is drawing concerns from Health Secretary Alex Azar, a former pharmaceutical executive who has called drug importation a "gimmick."

The President is embracing a controversial Florida proposal to import drugs from Canada, which Republicans have long opposed and many health experts have questioned.

The measure -- backed by Florida Republicans Gov. Rick DeSantis and Rep. Matt Gaetz, both close Trump allies -- requires federal approval. Trump has spoken highly of the idea and has told Azar to pursue the issue as a way to reduce the cost of prescription drugs.

But as recently as last week, Azar expressed reservations during a meeting with Trump, DeSantis and Gaetz, prompting a "spirited discussion," Gaetz told CNN.

"The President directed the secretary to work with Florida to get a plan approved," Gaetz said, who hopes the measure can then be replicated in other states. "I expect that will occur."

Trump has a long history of openly disagreeing with or disregarding his top officials on policy, like former Defense Secretary James Mattis and former Secretary of State Rex Tillerson. The differences with his health secretary -- a former George W. Bush administration official who came to his current role after a decade at drug giant Eli Lilly -- come as Trump is trying to deliver on his health care promises heading into the 2020 campaign.

The President openly championed the importation proposal while standing next to Azar later in the week during a White House event about surprise medical bills.

"And now [drug prices are] going to be going down a long way further, including the fact that we may allow states to buy drugs in other countries if we can buy them for a lesser price -- substantially less price," Trump said. "So we will allow them, with certain permissions, to go to other countries if they can buy them for 40, 50, 60% less."

The Department of Health & Human Services pointed to remarks Azar told reporters at a separate press conference last week -- that the Florida proposal would have to overcome certain hurdles before getting the green light.

"The President and I have been very clear: We support importation if it can be done safely and if we can deliver real savings to patients," Azar said. "We'll have to see what plan Florida comes up with or any other state."

The secretary's comments are a far cry from what he said about importation a year ago -- when he called it a "gimmick." He stressed that the idea has been reviewed multiple times by the Congressional Budget Office, which has said it would have "no meaningful effect" in large part because Canada's drug market is too small.

"Canada simply doesn't have enough drugs to sell them to us for less money, and drug companies won't sell Canada or Europe more just to have them imported here," Azar said in remarks about the President's blue print to lower drug prices last May.

Also, he added, the last four commissioners of the Food and Drug Administration have said there's no way to effective ensure that the medication is really coming from Canada, and not a counterfeit factory in China.

"The last thing we need is open borders for unsafe drugs in search of savings that cannot be safely achieved," he said. "You can't improve competition and choice in our drug markets with gimmicks like these."

Politico first reported on the meeting last week.

Azar is not the only administration official to express skepticism.

Scott Gottlieb, a Trump appointee who recently stepped down as FDA commissioner, poured more cold water on the idea Friday at a speech at the National Press Club, noting that the agency had issues with counterfeit drugs brought into the country by wholesalers in Florida. Even importing drugs because of shortages "ends up being a huge endeavor for the agency, not something that can be replicated on a wide scale," he said.

The agency formed a drug importation task force last summer, though Gottlieb stressed at the time that it would mainly be for addressing short-term shortages of specific medications, including disruptions caused by sudden significant price increases. The task force hasn't issued any public statements since.

DeSantis first announced the importation plan in February, saying drug costs are one of the biggest drivers of America's "out of control health care spending."

"While our prices remain high, our neighbors in Canada are spending signficantly less for the same drugs," said DeSantis, who has yet to sign the legislation. "These price disparities are indefensible and inexcusable and I am ready to act."

Gaetz is one of Trump's most visible defenders in the House. He has long held some unconventional views for a Republican, such as his support for legalizing the use of medical marijuana. DeSantis, who has yet to sign the importation bill, also allied himself closely with Trump during his campaign for governor and recently attended the President's campaign rally in hurricane-stricken Panama City.

Florida isn't alone. State lawmakers in Vermont last year passed a bill authorizing drug importation, but have yet to submit it to the Department of Health & Human Services for approval.

The issue of importing drugs from abroad has also split Republican leaders in the Senate.

Iowa Sen. Chuck Grassley, who leads the powerful Senate Finance Committee and has introduced bills that would allow importation for years, praised the creation of the FDA task force last summer, calling it "long overdue."

But asked about Trump's support of Florida's plan, Sen. Lamar Alexander of Tennessee, the chair of the influential Senate Health Committee, noted that FDA already allows importing drugs when it has approved the facility and the supply chain it takes to get the medicine to consumers.

"Each year, billions of prescriptions are written for Americans who count on the FDA's gold standard of approval that the manufacture and supply of each of those prescriptions is safe," he said.

Trump's embrace of the idea likely surprised Republicans, said Joe Antos, a health policy scholar at the right-leaning American Enterprise Institute. His support may stem from a political need to say they are doing something about drug prices , coupled with hearing about Americans turning to Canada for lower-cost drugs.

"This is one of a lot of ideas that he's willing to float trial balloons on," Antos said of Trump. "Whether or not they get in the air is another matter."