A railway spokesperson said the incident occurred near Walingdisa railway station in Karbi Anglong district, about 270 km east of Assam's main city Guwahati. The train was carrying petroleum products.
"The train hit the elephant herd squatting on the track. The train driver probably did not see the herd because of dense fog," Northeast Frontier Railways chief spokesperson S. Hajong told IANS.
Witnesses said the crash cut the calves after dragging them for about 200 metres.
"The two adult elephants were in a pool of blood after being hit by the train," said Narayan Das, a wildlife ranger.
Soon after the accident, hundreds of locals armed with crude implements arrived at the site and took away the nails, tusk and other body organs of the dead animals.
"When we reached the site, we found body organs of the elephants missing," Das said.
Experts say that wild elephants have been moving out of the jungles in search of food because people have been encroaching animal corridors. This has led to increasing elephant attacks on villages.
Elephants have killed 270 people in Assam in the past five years. A total of 280 elephants have died in the same period, many of them victims of retaliation by people, according to the wildlife department.
Assam has India's largest population of Asiatic elephants estimated at around 5,500.