Jorge Vinicio Orantes Sosa (hore-HAY' Vin-EE'-see-OH' ORR'-ent-EHS' SOH'-sah) was arrested in Lethbridge, Alta., in January, 2011.
He is accused of lying to immigration officials about his military past when he applied for U.S. citizenship.
Sosa, who has Canadian citizenship as well, is also wanted by Guatemalan authorities for allegedly taking part in a village massacre in the Central American country in 1982.
In a written decision, Justice Brian O’Ferrall said Sosa's request to appeal the extradition order is denied.
He says a review of the case indicates an appeal is hopeless and there is no injustice in requiring Sosa to answer perjury charges in the United States.