Koshik can reproduce "annyeong" (hello), "anja" (sit down), "aniya" (no), "nuwo" (lie down) and "joa" (good), the paper says.
One of the researchers said there is no conclusive evidence that Koshik understands the sounds he makes, although the elephant does respond to words like "anja."
Everland Zoo officials in the city of Yongin said Koshik also can imitate "ajik" (not yet), but the researchers haven't confirmed the accomplishment.
Koshik is particularly good with vowels, with a rate of similarity of 67 percent, the researchers said. For consonants he scores only 21 percent.
Researchers said the clearest scientific evidence that Koshik is deliberately imitating human speech is that the sound frequency of his words matches that of his trainers.
Vocal imitation of other species has been found in mockingbirds, parrots and mynahs. But the paper says Koshik's case represents "a wholly novel method of vocal production" because he uses his trunk to reproduce human speech.
In 1983, zoo officials in Kazakhstan reportedly claimed that a teenage elephant named Batyr could reproduce Russian to utter 20 phrases, including "Batyr is good." But there was no scientific study on the claim.
Researchers believe Koshik learned to reproduce words out of a desire to bond with his trainers after he was separated from two other elephants at age 5.
Koshik emerged as a star among animal enthusiasts and children in South Korea after Everland Zoo claimed in 2006 that he could imitate words, two years after his trainers noticed the phenomenon. His growing reputation prompted Austrian biologist Angela Stoeger-Horwath and German biophysicist Daniel Mietchen to study him in 2010, zoo officials said.
Oh Suk-hun, a South Korean veterinarian who co-authored the research paper with Stoeger-Horwath and Mietchen, said the elephant apparently started imitating human speech to win the trust of his trainers.
In April, a children's science book called "Joa Joa, Speaking Elephant" was published. The cover photo showed Koshik opening his mouth wide while raising a trunk over his trainer's head.
Researchers said Koshik was trained to obey several commands and "exposed to human speech intensively" by trainers, veterinarians and zoo visitors.
Shin Nam-sik, a veterinary professor at Seoul National University who has seen Koshik, agreed with researchers' finding that the elephant was able to mimic human speech.
"In Koshik's case, the level of intimacy between him and his trainer was the key factor that made the elephant want to sound like a human," Shin said.
Kim Jong-gab, Koshik's chief trainer, said the elephant was timid for a male when he first came to Everland Zoo, so trainers often slept in the same area with him. Kim thinks that contact helped Koshik feel closer to humans.
Kim said he has another phrase he wants to teach Koshik: "Saranghae," or "I love you."