Preliminary reports indicate that at least five people died in a landslide in J&K's Doda district, while another person was swept away by a swollen rivulet in Himachal's Kangra district.
Meanwhile, rescue operations are on, but some are feared missing.
Details of the situation in Kashmir
The deaths in Jammu & Kashmir's Doda district resulted out of a landslide hitting a nomad family's mud house.
The incident killed all five in the family. Among the dead were three minors.
Authorities have announced Rs. 4 lakh compensation for the next of kin of each of the dead.
Meanwhile, 29 people have been rescued from various parts of the flood-hit Kathua district.
Himachal Pradesh has been badly hit
Himachal Pradesh seems to have been badly hit after torrential rains in the state lasted 24 hours.
A 'high alert' has been issued for Kullu, and the Indian Air Force (IAF) and the Indian Army are carrying out rescue operations.
Manali has been cut off from Kullu as several highways and roads remain blocked from landslides and overflowing rivers.
Schools were closed on Monday.
Rainfall in Himachal over the past 24 hours
According to Shimla Met Centre data from Monday morning, Dalhousie in the Chamba district received 170mm rain in the past 24 hours, followed by Manali (121mm), Kangra (120.8mm), Chamba (117mm) Palampur (108mm), Dharamshala (62.6mm), Una (62mm), and Shimla (23.1mm).
While several have been rescued, some remain missing
Following torrential rain on Sunday, an IAF helicopter had rescued 19 people from the Kullu district after flash floods struck.
The Army has also been called in to rescue two people stranded in flash floods in Himachal's Kangra district.
Meanwhile, nine researchers from West Bengal who had gone to the 5,480m high Gangstang glacier have also gone missing in Himachal.
Dams have been opened, Chandigarh-Manali highway is blocked
Additionally, following torrential rains on Sunday, authorities in Himachal Pradesh opened the gates of four dams - Larji, Pandoh, and Sanan in Mandi, and Chamera in Chamba - thereby making the situation downstream even worse.
Rising water levels in the Beas river near Aut has also resulted in the Chandigarh-Manali national highway getting blocked.