Two avalanches swept through army camps in Dawar and Sonamarg, both near the heavily-militarised Line of Control that divides Kashmir between India and Pakistan.
A defence spokesman who declined to be named said that six soldiers were killed at Dawar and 15 others were dug out of the snow, while three soldiers died at Sonamarg, a popular destination for Indian tourists in the summer.
"Efforts are underway to rescue the trapped soldiers whose exact number is being ascertained," said Lieutenant Colonel J.S. Brar, the military spokesman in the Indian Kashmir summer capital Srinagar.
The mountainous, Muslim-majority region of Kashmir was split in two in the aftermath of independence on the subcontinent when British rule ended in 1947.
Both India and Pakistan claim the whole territory, which is divided by the de facto border known as the Line of Control.
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