Helicopters were deployed to rescue people cut off by flash floods that revived memories of 2014, when the Jhelum River flowing through the region's main city, Srinagar, burst its banks, swamping homes and killing 200 people.
Snowfalls triggered multiple avalanches, defense spokesman Rajesh Kalia told Reuters.
"A post in Batalik sector was buried," he added. "Two out of five soldiers have been rescued. A rescue operation for three soldiers was in progress and three bodies have been recovered."
Rajiv Pandey, senior superintendent of police in Poonch, said 17 people were evacuated from the area.
In Srinagar, the summer capital of the state of Jammu and Kashmir, some low-lying districts along the Jhelum were swamped but residents said the river was starting to recede.
"We are relieved as the water level is receding and the rains are reducing," said one resident. "We are praying that rain should stop."