Prosecutors are appealing the dismissal of charges that Luis Posada Carriles made false statements as part of his bid to become a naturalized U.S. citizen.
Posada is a Cuban-born citizen of Venezuela, where he is wanted for alleged involvement in a 1976 airliner bombing that killed 73 people. He denies any wrongdoing.
U.S. prosecutors say he was taken into custody after he illegally entered the U.S. from Mexico in 2005.
In dismissing the immigration charges last year, U.S. District Judge Kathleen Cardone in El Paso, Texas, said federal authorities engaged in trickery and deceit by using a naturalization interview to build a criminal case against Posada.
Cardone also ruled that transcripts of Posada's April 2006 interview could not be used as evidence in the criminal case. The judge said the interview was tainted by a translator's mistakes interpreting for Posada.
Federal prosecutors argued Wednesday before the 5th U.S. Circuit Court of Appeals in New Orleans that Cardone should not have taken the case out of a jury's hands. John De Pue, a lawyer for the Department of Justice's national security division, said Cardone went too far in tossing out the entire transcripts of the interview.
"It's our submission that no one could have possibly misunderstood any of these questions," he told the court's three-judge panel.
Rhonda Anderson, a lawyer for Posada, said it was Cardone's job to review the reliability of evidence before a jury could hear it.
"The court exercised its proper authority under the federal rules of evidence," she said.
A ruling could take several months.
Posada, who moved to Miami after the criminal case was dismissed, still faces a deportation order.
An immigration judge in El Paso has ruled that he should be deported, but not to Cuba or Venezuela.
The governments of both countries want him handed over to face charges that he plotted the airliner bombing. The former CIA operative and U.S. Army soldier is also accused of participating in a series of 1997 bombings targeting tourist spots in Havana.
He was convicted in Panama of participating in a 2000 plot to assassinate former Cuban president Fidel Castro, but released in 2004 as part of a general amnesty.