The man, with long beard and hair, was discovered Thursday when his 24-foot fibreglass boat with propellerless engines floated onto the reef at Ebon Atoll and he was spotted by two locals.
"His condition isn't good, but he's getting better," Ola Fjeldstad, a Norwegian anthropology student doing research on Ebon, told AFP by telephone.
Fjeldstad said the man, dressed only in a pair of ragged underpants, claims he left Mexico for El Salvador in September 2012 with a companion, who died at sea several months ago.
Details of his survival are sketchy, Fjeldstad added, as the man only speaks Spanish, but he said his name was Jose Ivan.
"The boat is really scratched up and looks like it has been in the water for a long time," said the researcher. "He has a long beard and hair."
Ivan indicated to Fjeldstad that he survived by eating turtles, birds and fish and drinking turtle blood when there was no rain.
No fishing gear was on the boat and Ivan suggested he caught turtles and birds with his bare hands. There was a turtle on the boat when it landed at Ebon.
Stories of survival in the vast Pacific are not uncommon.
In 2006, three Mexicans made international headlines when they were discovered drifting in the middle of the ocean in their stricken boat, nine months after setting out on a shark-fishing expedition.
And in 1992, two fishermen from Kiribati were at sea for 177 days before coming ashore in Samoa.
According to Fjeldstad, the Marshall Islanders who found Ivan took him to the main island on the atoll to meet Mayor Ione de Brum, who put in a call to the Ministry of Foreign Affairs in Majuro.
Officials at the Foreign Ministry said Friday they were waiting to get more details and for the man to be brought to Majuro.
The government airline's only plane that can land at Ebon is currently down for maintenance and is not expected to return to service until Tuesday at the earliest, with officials considering sending a boat to pick up the castaway.
"He's staying at the local council house and a family is feeding him," said Fjeldstad, who added that the man had a basic health check and was found to have low blood pressure.
But he did not appear to have any life-threatening illness and was able to walk with the aid of men on the island.
"We've been giving him a lot of water, and he's gaining strength," said the Norwegian.