But the embassy said in a statement that "we are extremely grateful to the Government of Mexico for its prompt assistance in the operation to rescue two USA citizen climbers".
Best known as Pico de Orizaba, the 5,610-meter mountain on the border between the states of Puebla and Veracruz attracts professional climbers from around the world as well as poorly equipped amateurs.
A Puebla official who was not authorized to be quoted by name said both climbers were U.S. citizens, but the U.S. Embassy did not immediately respond to requests to confirm their nationalities or hometowns.
The embassy employee was rescued Monday afternoon and is now hospitalized in Mexico City, according to the Mexican official. "Unfortunately, one of the climbers passed away".
Freddy's body was recovered and brought down the mountain by foot Tuesday morning, ABC News reported.
The cause of their accident is under investigation.
Today the US embassy said the climbers were members of its diplomatic mission.
The State Department would not say in what roles the two employees worked in Mexico or provide other details, citing privacy concerns.
In November, an American was killed after suffering a fall by the sub-zero temperatures, according to the Associated Press, and nine others had to be rescued amid icy conditions.