"Ecuador will call on ... OAS Secretary (General José Miguel Insulza) for a definite solution to the case," the ministry statement said.
Juan Manuel Santos, Colombia's defence minister, confirmed on Sunday that the man - one of several people to die in the March 1 attack - was Ecuadorean.
Santos also said that an individual was found to have been helping members of the Revolutionary Armed Forces of Colombia (Farc), a charge which Franklin Aisalla's father, Guillermo, dismissed as a lie.
The charge prompted Hugo Chavez, the Venezuelan president, to warn Colombian officials to watch their words or risk a new diplomatic flare-up, and to accuse Santos of rekindling tensions with Ecuador.
"For the love of God," Chavez said, directing his advice at Alvaro Uribe, the Colombian president, "take good care with spokesmen of war like your defence minister [Santos]."
Wellington Sandoval, Ecuador's defence minister, earlier said that relations with Colombia had "become complicated, because an Ecuadorean has died in an attack by a foreign country".
"The issue has become more difficult" he said after Aisalla's identification.
Bogota said it was awaiting the arrival of investigators from Ecuador who are looking into the death of Aisalla.
Colombia's raid on a camp run by Farc inside Ecuador killed several suspected rebels besides Reyes.
The cross-border strike sparked a diplomatic crisis that threatened to engulf much of Latin America.
The dispute temporarily led to a rupture in relations between Colombia and its neighbours Ecuador and Venezuela, who both mobilised their armed forces to their borders with Colombia.
Ecuador has yet to resume diplomatic relations with Colombia.