When Fidel Castro first met Che Guevara in Mexico City in 1955, they began planning a guerrilla war that would sweep Cuba and change the course of Latin American history.

Mr. Castro became Cuba’s Communist leader, defying the United States for decades. Mr. Guevara, an Argentine, became a legend to his supporters and enemies alike, even after he was executed in Bolivia in 1967. In 2017, Mexicans commemorated their meeting with statues, linking Mexico to a pivotal moment in the Cold War.

But the statues were removed last week by a local Mexico City mayor, setting off a political firestorm that has drawn in the country’s president and reignited a debate about how to recognize a divisive history.

The local mayor, Alessandra Rojo de la Vega, said the statues were improperly installed and that the men should not be honored, calling them “murderers” who “continue representing a lot of pain.” She pointed to people who were silenced, jailed and killed under Mr. Castro’s nearly half-a-century reign, and to how Cuba still struggles with food and electricity shortages.

“I understand that there are people who see Fidel and Che as their revolutionary figures, but governing isn’t about choosing which victims to show solidarity to,” Ms. Rojo de la Vega said in an interview.