WASHINGTON — President Trump on Tuesday expelled 15 Cuban diplomats, escalating his response to a mysterious affliction that has stricken American Embassy personnel in Havana in a move that cast a Cold War chill over relations between the two countries.

The order to the diplomats to leave the United States constituted the latest in a series of actions by Mr. Trump to unwind the détente between the United States and Cuba undertaken by his predecessor, President Barack Obama. Mr. Obama sought to end the hostility and mistrust that had characterized the relationship between the two countries for more than a half-century, and regarded the resumption in relations as one of his foreign policy legacies.

The Cuban government condemned what it called a “hasty, inappropriate and unthinking” decision motivated by politics, and warned that the diplomatic dispute would sour relations already imperiled by Mr. Trump’s move to crack down on travel and commerce with the island nation.

The State Department said the expulsion of the diplomats was intended to force Cuba to place its embassy in Washington, where the diplomats were stationed, on the same emergency status that the United States is now operating under in Havana after it decided last week to pare its staff there down to a skeletal group of just 27 people.