David Kris, assistant attorney general for national security, described the couple's alleged spying for the communist government as "incredibly serious".
Kendall and Gwendolyn Steingraber Myers' arrest comes as the US attempts to ease tensions with Cuba dating from the Cold War.
A senior State Department official described the potential for damage as great and the timing unfortunate.
The couple, who lives in Washington, were arrested Thursday and pleaded not guilty Friday in US District Court.
Cuba snubs OAS
A senior communist official says Cuba is happy with the Organisation of American States (OAS) decision lifting a decades-long suspension on the island, but it will not return to the group.
Cuban parliament chief Ricardo Alarcon has told reporters at an unrelated Thursday event that the OAS decision in Honduras on Wednesday corrected a long-standing "injustice." The United States joined Latin American nations in voting for the measure.
The OAS suspended Cuba from the body at the height of the Cold War in 1962 because Cuban leaders embraced Marxist principles.
Both President Raśl Castro and his ailing older brother Fidel, who resigned last year, have criticised the OAS and say Cuba will not rejoin.