Transferred to the United States, he was appointed Argentine Consul General to San Francisco and later New York, where he remained until his father's death in 1952 compelled him to return to the family business in Mendoza.

Close to President Juan Perón since his days in the Soviet Union, Orfila was appointed Ambassador to the United States by the populist Argentine leader, back in power in 1973 after an 18-year-long exile.

Preferring his own brand of "gala diplomacy" to confrontation, Orfila was fond of enlisting his sumptuous beltway home for diplomatic dinners in the interest of assuaging differences.

Orfila rallied support in the OAS for Carter's campaign pledge to renegotiate U.S. presence in the Panama Canal Zone, a contentious issue across Latin America.

Working with President Carter and the U.S. Assistant Secretary of State for Human Rights, Patricia Derian, he marshalled the then-dormant Inter-American Commission on Human Rights into investigations inside repressive regimes like his own country's, the Argentine military junta; after looking into allegations of widespread political murders and kidnappings in September 1979, the commission's 1980 report removed any doubts as to the state of freedoms in the country at the time, and helped lead to an improvement in the climate of civil liberties.

With violence in the region more concentrated in Central America after 1980, Orfila lost a valuable ally in his efforts to mediate the area's civil wars when Panamanian strongman Omar Torrijos' plane exploded in August 1981.

Increasingly unable to exert credibility despite the lack of evidence for the allegations, on 21 June 1984, Secretary General Orfila resigned his post, expressing frustration over the OAS' inability to influence U.S. Latin American policy during the 1980s.