President Trump’s decision to move a step closer to imposing tariffs on imported medicines poses considerable political risk, because Americans could face higher prices and more shortages of critical drugs.

The Trump administration filed a federal notice on Monday saying that it had begun an investigation into whether imports of medicines and pharmaceutical ingredients threaten America’s national security, an effort to lay the groundwork for possible tariffs on foreign-made drugs.

Mr. Trump has repeatedly said he planned to impose such levies, to shift overseas production of medicines back to the United States. Experts said that tariffs were unlikely to achieve that goal: Moving manufacturing would be hugely expensive and would take years.

It was not clear how long the investigation would last or when the planned tariffs might go into effect. Mr. Trump started the inquiry under a legal authority known as Section 232 that he has used for other industries like cars and lumber.

Mr. Trump said in remarks to reporters on Monday that pharmaceutical tariffs would come in the “not too distant future.”

“We don’t make our own drugs anymore,” Mr. Trump said. “The drug companies are in Ireland, and they’re in lots of other places, China.”