HHS wants US prescription drug prices to drop to the lowest possible price among countries that are members of the Organisation for Economic Co-operation and Development, which includes most of the world's largest economies.
The new pricing targets would focus on OECD countries that have a gross domestic product per capita of at least 60 per cent of US per-capita GDP, the department said.
Trump wants prescription drug prices to drop by between 59 per cent and 90 per cent.
Wall Street analysts and legal experts have said his order would be difficult to implement and is likely to face legal challenges.
Trump tried in his first term to bring drug prices in the United States in line with other countries but was blocked by the courts.
The US pays by far the most for prescription medicines, often nearly three times more than those in other developed countries.
"The idea here is that within that set of fairly developed countries the US wants to be the most favoured nation," said Yunan Ji, assistant professor at Georgetown's McDonough School of Business.
Japan, Canada and some countries in western Europe meet the 60 per cent threshold that HHS has laid out.
Smaller OECD countries like Estonia or Costa Rica would fall short of that criteria.
Ji said that a most favoured country pricing policy usually works in a small market but if the US tries to implement such a policy, it could change the "global equilibrium" since it is the largest prescription drug market.
"It's almost certain that drug manufacturers will have to renegotiate their contracts with other countries," she added.
The US also invests heavily in pharmaceutical research and development and drug makers have said drastic price cuts would stifle R&D and innovation.
The agency said US Health Secretary Robert F Kennedy Jr and Centers for Medicare and Medicaid Services Director Mehmet Oz will share their specific targets for medicine manufacturers in the coming weeks.
"We expect pharmaceutical manufacturers to fulfil their commitment to lower prices for American patients, or we will take action to ensure they do," Kennedy said on Tuesday.
Trump's order also directs the government to consider direct-to-consumer purchasing programs that would sell drugs at the prices other countries pay.
