Komsomolskaya Pravda said over 20,000 zerens, a species of antelope, have managed to cross the fence on the Mongolian side but have become entangled in the three-meter-high fence on the Russian side, and have died of injuries and thirst.
The animals have been trying to reach Russia's Daursky nature reserve just across the border, which is rich in vegetation and water.
The paper quoted the head of the nature reserve, Alexander Borodin, as saying such a vast migration from the Mongolian steppes has never been seen before.
"There are now around 100,000 zerens moving toward our border. If they all die on the neutral territory near our border, an environmental catastrophe will be unavoidable."
On Tuesday Russia's environmental watchdog Rosprirodnadzor asked the governor of the Chita Region to provide water for the zerens.
The paper said the Daursky nature reserve lacks the equipment and funds to transport such a large volume of water, and that even if the border is opened, most of the animals will be too weak to reach the nearest lakes.
Zerens are classified as "conservation dependent" on the International Union for the Conservation of Nature and Natural Resources' Red List of threatened species.
