U.S. allies' drug pricing strategies are not sustainable for long-term success, and that's adversely leading to higher prescription costs at home and abroad, FDA Commissioner Dr. Scott Gottlieb told CNBC on Tuesday.

Europeans "do underpay relative to us for branded drugs and that's in part because they do put price controls and utilization restrictions on those drugs," Gottlieb said in a "Squawk Box" interview. "But they're overpaying relative to us on generic drugs."

"That's not a system for success in the long run," he argued. "So, I don't think they're set up for long-term success."

President Donald Trump on Friday criticized foreign allies, accusing them of paying less than the United States for prescription drugs while benefiting from American investment in research and drug development. He said he has directed U.S. Trade Representative Robert Lighthizer to make fixing this a top priority with every trading partner.

Gottlieb, who was praised by Trump during his speech Friday on how to lower prescription drug prices in the U.S., said the issue of "intellectual property appropriation" needs to be addressed on a trading level. "It's well above my pay grade in terms of having those discussions," Gottlieb added.

However, he said the U.S. also wants to make sure it adequately rewards companies that take on the risk of developing new drugs that may or may not work out.

"We do think the market-based system gives appropriate incentives and rewards for people to take the risk and innovate," he said. "The problem becomes when there's a lack of competition because of government rules that prevent the competition from taking place."

The idea behind the Trump plan is drug companies should raise prices overseas where governments subsidize costs and lower prices in the U.S.

However, not everyone was enthused about Trump targeting foreign countries.

Former Health and Human Services Secretary Tommy Thompson, who praised Trump for addressing the issue of high drug prices, told CNBC on Friday the president's possible strategy to push for increases in drug prices in foreign countries wouldn't work.

"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."