(Adds new attack)

SRINAGAR, India, July 20 (Reuters) - Two Indian soldiers, including an officer, and four suspected Muslim militants were killed in separate gun battles in Kashmir, while two others died in a grenade attack, the army said on Sunday.

The violence flared up across the Himalayan region ahead of a new round of India-Pakistan peace talks on Monday that are opposed by Kashmiri separatist militants.

The two soldiders died in a firefight with militants in Rajouri area of south Kashmir, a day after nine Indian troops were killed in a landmine blast near Srinagar.

"The encounter broke out on Saturday and still continues," Indian army spokesman Lieutenant Colonel S. D. Goswami said.

Separately, an Indian tourist and a local picnicker were killed and at least five others wounded on Sunday when suspected Muslim militants threw a grenade at a hill resort in Gulmarg, west of Srinagar, police said.

The valley of Gulmarg, ringed by pine forests and famous for its ski slopes and cable car, lies close to the Line of Control dividing Indian and Pakistani Kashmir.

No militant group has claimed responsibility for the attack.

Four suspected militants were shot dead by soldiers on Saturday when they tried to sneak in from Pakistan in Kupwara sector, northwest of Srinagar, the summer capital of Kashmir.

India and Pakistan both claim Kashmir, and have fought two wars over the Himalayan region.

They launched a peace process in 2004 but made little progress on their main dispute over Kashmir, where tens of thousands of people have been killed since a separatist revolt against New Delhi's rule erupted in 1989.

New Delhi says Islamabad has not done enough to curb Muslim militants operating from its soil, a charge Islamabad denies. (Reporting by Sheikh Mushtaq, Editing by Krittivas Mukherjee) (For the latest Reuters news on India see: http://in.reuters.com; for blogs see: http://blogs.reuters.com/in/)

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