A defence ministry statement said the 20,000 were rescued in different regions of the state.
The army has deployed 205 columns for rescue and relief work and given away 4,000 blankets and 90 tents to victims of the worst floods to hit the state in half a century.
“The army also distributed 23,000 litres of water and 600 kg biscuits in the flood-affected areas,” the statement said.
It said 60 medical teams of the Armed Forces Medical Services had swung into action.
Naval marine commandos rescued around 200 people at Haigaon on the Srinagar-Sopore highway.
Naval diving teams are on standby in New Delhi, Mumbai and Vishakhapatnam to proceed to Jammu and Kashmir.
A total of 45 aircraft and helicopters have been pressed into service.
The ministry said 85 tonnes of medicines have been airlifted for the flood victims and 16 relief camps had been set up in the state.
The Indian Air Force has rescued 1,245 people using helicopters and transport aircraft. “So far 140 sorties were undertaken by the helicopters and aircraft and 155 tonnes of relief materials have been dropped.”