The source said the incident occurred on Sunday at 6:30 pm [15:30 GMT] in the southern Russian republic.
"The serviceman killed his platoon commander and two other soldiers with an [AK-47] assault rifle and then attempted to commit suicide by shooting himself in the head with the same weapon," the source said.
The soldier is now in a critical condition in hospital. An investigation into the incident has been launched.
In another incident in Chechnya, a soldier was killed by a bomb during a minesweeping operation on Sunday. A search for other explosives in the area is continuing.
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The growing outright rivalry between the United States and China gives Russia more foreign policy weight, enabling it to assume the role of a balancer. So far it has been doing so rather skillfully. Today it may participate in a joint naval exercise with China that Beijing positions as outwardly anti-American. But tomorrow it can team up with the naval forces of the Old World.