President Donald Trump's plan to bring down drug prices at home by forcing higher prices abroad won't work, former Health and Human Services Secretary Tommy Thompson said Friday.

Trump unveiled his administration's plan to lower prescription drug prices on Friday. During his speech from the White House, Trump criticized foreign countries for paying less than the U.S. for prescription drugs, saying it's time to end "global freeloading once and for all."

Thompson, who spoke in an interview with CNBC's "Power Lunch" before Trump's speech, praised the president and the current HHS secretary, Alex Azar, for "keeping their word" and addressing the issue of high drug prices in the U.S.

But when asked whether Trump's strategy to raise prices on foreign countries would work, he said, "Of course it wouldn't."

"Just raising the prices across the world isn't going to help America," said Thompson, who served as HHS secretary from 2001 to 2005 under President George W. Bush. "It's just going to increase prices for other people."

Former HHS Secretary Kathleen Sebelius, who said she spoke with Azar on Thursday about the drug-pricing plan, also took issue with Trump's plan to raise prices on foreign countries. She told "Power Lunch" that U.S. drug prices aren't a foreign issue.

"That doesn't do anything for American consumers," said Sebelius, who served as HHS secretary under former President Barack Obama. "There's no question American consumers pay the highest prices in the world. But that's because we don't have a drug-pricing policy."

On Friday, Trump also criticized drugmakers and middlemen such as pharmacy benefit managers. So-called PBMs negotiate drug benefits for insurance plans and employers.

Earlier Friday, Azar told CNBC's "Squawk Box" that everybody's gaining something from higher list prices except patients and taxpayers. "We have to fundamentally examine and re-examine the role of pharmacy benefit managers," he added.

— CNBC's Angelica LaVito contributed to this report.