(New throughout, adds details, background and comments from Peru's president, military official, spokesman for Chile)
LIMA, Feb 19 (Reuters) - Two Peruvian naval officers face treason charges on allegations that they spied for Chile, a case that threatens to derail newly improved relations between the two Andean countries, Peru said on Thursday.
Military courts in Peru are trying two officers and investigating a third for allegedly spying for historic rival Chile, Defense Minister Pedro Cateriano said.
President Ollanta Humala said confirmation of the spying would be "very, very serious for bilateral relations between Peru and Chile, which we have been strengthening."
"This cannot go away just like that," Humala told reporters on the sidelines of an event.
Chile, a historic enemy of Peru and today its biggest Latin American trade partner, said it had not been officially notified by Lima of the spying case.
"At any rate, relations between Peru and Chile are going through a period of strengthening," said Alvaro Elizalde, spokesman for Chilean President Michelle Bachelet's government.
Last year, a landmark international court ruling settled an old maritime border dispute between the neighboring countries, raising expectations that their long history of distrust had passed.
Chile's military is suspected of paying the men to gather confidential information after recruiting them with agents disguised as Italian businessmen, local broadcaster America TV reported on Wednesday.
One of the men on trial was paid $200 for each report on Peruvian fishing that he turned in, America TV reported.
Chile and Peru are both major exporters of fish and fishmeal and have previously disputed the rights to productive waters in the Pacific.
The two officers also sent emails with encrypted messages that could have compromised national security, said Juan Ramos Espinoza, the head of Peru's military courts.
Ramos said ongoing investigations have yet to determine if higher-ranking officers were also involved in spying.
Frequent trips abroad alerted intelligence agents to the men's activities and led to their arrest last year, Cateriano said.
"We urge the military justice system to act swiftly and if it finds them responsible to apply the maximum penalty," Cateriano said at a press conference.
Treason during peacetime carries a sentence of up to 25 years in Peru.
Former presidents Alejandro Toledo and Alan Garcia, an outspoken critic of Humala, said they would meet with the government late on Thursday to discuss the scandal. (Reporting by Mitra Taj and Ursula Scollo, Additional Reporting by Fabian Cambero in Santiago; Editing by David Gregorio)