The dead include four children, a senior administrative officer told IANS.
Most of those killed were either washed away by swollen streams or killed in house collapses.
"Six were killed in house collapse accidents and four were washed away by swollen streams in Gool and Mahore areas of Jammu region," the official said.
He said 24 people trapped by swollen rivers have been rescued while 200 families have been shifted to safer places in Poonch and Rajouri districts.
Incessant rains for the last two days have swollen all rivers and streams in Jammu region, damaging roads, bridges, railway tracks, houses and government properties.
The Jammu-Udhampur rail link was closed Thursday because of landslides.
The Srinagar-Jammu highway was also closed because of landslides at several places on the highway that forms the landlocked Valley's only road link with the rest of the country.
Both the Tawi and the Chenab rivers in Jammu region were flowing with full fury Thursday morning.
Meanwhile, the Jammu and Kashmir Met office has forecast light to moderate rain at many places in Jammu region Thursday, warning that a heavy downpour could also occur at some places.