The bus skidded off a road in the remote Kishtwar region and fell into a deep, narrow valley, senior police official M K Sinha said.
Twenty passengers died instantly and 10 others were badly injured, Sinha told AFP.
Seven of those were in critical condition and were evacuated to a nearby hospital.
Road accidents are common in the mountainous parts of the northern state of Jammu and Kashmir, owing to its rugged terrain, with speeding and overcrowding adding to the safety hazards.
A separate crash on Monday in neighbouring Himachal Pradesh killed three school students and their driver, the Press Trust of India reported.
Last week, 11 students on their way to a picnic were killed when their bus fell into a gorge in Shopian district of Kashmir, officials said.
Some 150,000 people die in road accidents on average each year in India, according to official figures.
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