In 1921, after World War I, Congress wanted to find a way to reflect the nation's gratitude to the many unknown dead who fought in the Great War, so they passed a series of acts authorizing Medals of Honor for the unknown casualties of not only the American Expeditionary Forces, but also the unknown casualties of European allies.
Oddly enough, the first act of Congress to award Medals of Honor to unknown soldiers was for Great Britain and French soldiers, not American. On March 4, 1921, an act was approved that...
...the President of the United States of America be, and he hereby is, authorized to bestow with appropriate ceremonies, military and civil, the Congressional Medal of Honor upon the unknown, unidentified British soldier buried in Westminster Abbey, London, England, and upon the unknown, unidentified French soldier buried in the Arc de Triomphe, Paris, France....
The act approving a Medal of Honor for the unknown American followed just a few months later, in August.
By virtue of an act of Congress approved 24 August 1921, the Medal of Honor, emblem of highest ideals and virtues is bestowed in the name of the Congress of the United States upon the unknown American, typifying the gallantry and intrepidity, at the risk of life above and beyond the call of duty, of our beloved heroes who made the supreme sacrifice in the World War. They died in order that others might live....
An award for the "unknown, unidentified Italian soldier to be buried in the National Monument to Victor Emanual 11, in Rome," was approved that October. A Medal of Honor for the unknown Belgian soldier was approved in December 1922, and an act was approved for the Romanian unknown soldier in May 1923.
French Marshall Joseph Joffre inspects Romanian troops during World War I. Romanian forces fought alongside Americans during the war, and Congress approved a Medal of Honor for their unknown deceased in 1923. No award for the unknown deceased of an allied force has been approved since.
The wording for each international award differs slightly — the act for the British and French unknown was "animated by the same spirit of comradeship in which the American forces fought alongside these Allies," while the Italian act cites the "spirit of friendship," — but all of the awards to allied unknowns were due to the American "desire to add whatever we can to the imperishable glory won by their deeds and to participate in paying tribute to their unknown dead."
Congress has not approved a new award for the unknown deceased of allied forces since 1923, but it has approved a new award of the Medal of Honor for the unknown Americans interred from World War II, the Korean War, and the Vietnam War. The acts were approved in 1948, 1957, and 1984.
Note that while the unknown deceased are interred at the Tomb of the Unknown Soldier, the acts approving the Medals of Honor are worded to honor the deeds of the "unknown American" and apply to all unknown Americans who died in service to their country in the respective theater of war.
The unknown American selected from the Vietnam War was later identified as Air Force 1st Lt. Michael Joseph Blassie. When Blassie's remains were returned to his family, it was decided that the Medal of Honor should remain at the Tomb of the Unknown Soldier, since the award was approved to honor the deeds of all unknown deceased who gave the ultimate sacrifice.