14 February 2019 09:25 pm
Police told the BBC that a car filled with explosives rammed a bus carrying the troops to the main city of Srinagar.
The Pakistan-based Islamist group Jaish-e Mohammad said it carried out a suicide bombing.
It is the deadliest attack on Indian forces in disputed Kashmir for years.
The blast took place on the heavily guarded Srinagar-Jammu highway about 20km (12 miles) from Srinagar.
"It's not yet clear how many vehicles were in the convoy. A car overtook the convoy and rammed into a bus with 44 personnel on board," a senior police official told BBC Urdu's Riyaz Masroor.
The official said the death toll might increase because dozens were "critically injured". The Central Reserve Police Force confirmed to the BBC that at least 34 of its personnel had been killed in the attack.
Indian Prime Minister Narendra Modi said it was a "despicable" and "dastardly" attack.
The AFP news agency said Jaish-e Mohammad had sent a statement to local media saying it was behind the attack.
Prior to Thursday's bombing, the deadliest attack on Indian security forces in Kashmir this century came in 2002, when militants killed at least 31 people at an army base in Kaluchak near Jammu, most of them civilians and relatives of soldiers.(BBC)