The bodies were discovered in a glacier on Pico de Orizaba, Mexico’s highest peak, after a head and a hand were spotted protruding from the ice at an altitude of 17,290 feet (5,270m).
A team of climbers who set out to investigate the discovery found two corpses, one seemingly clinging to the other.
Both bodies are thought to be those of two Mexican climbers who disappeared in 1959 when a team of seven were caught in an avalanche.
Four of them survived but three were reported missing, presumed dead, and it is thought that a third body might be found when recovery teams are able to return to the peak.
Luis Espinoza, 78, was one of the 1959 team who was caught in the avalanche but managed to dig himself out of the ice and snow and to reach safety.
Pico de Orizaba is Mexico's highest peak (AFP/Getty)
After studying photographs of one of the bodies on the mountain he said he was confident that they were those of two of his missing friends.
The corpses appeared to have been partly mummified, with skin and muscle tissue and some clothing visible. Glaciers have been known to preserve bodies for years – sometimes thousands of years such as the Tyrolean Ice Man who was found in 1991 on the border of Austria and Italy 5,000 years after he was killed by an arrow.
Juan Navarro, the mayor of Chalchicomula de Sesma, the town nearest Pico de Orizaba, said: "It all leads to think this was the 1959 expedition in which they disappeared. I believe there should be another corpse, because three were reported [in the avalanche].
"The ice is crystalized, they are practically planted in concrete. The idea is to get them out ... but yesterday the weather was a bit complicated, because of the fog.
"It is a very difficult area where people normally don't go. It is an area where there is only snow, and no route."
The mountain is a dormant volcano which is thought to have last erupted between 1545 and 1566 and the first known ascent – locals may have done it earlier – was by two US soldiers, William Raynolds and G Maynard, in 1848. Mount Kilimanjaro is the only dormant volcano that is higher.
Officials from Chalchicomula de Sesma hope to be able to use a government helicopter to bring the corpses down, once they are dug out of the ice.
The head and hand protruding from the ice were spotted by a climbing team a few days ago and it was realised they were from two bodies when a recovery team was sent up the mountain to dig out the remains.
The bodies were found just over 1,000 feet down from the 18,406 feet (5,610m) summit. DNA tests are likely to be used to help identify the bodies once they are recovered.
