"There are people in the valley who want the cycle of deaths and killings to continue... I don't want them to win," Abdullah was quoted by the Press Trust of India news agency as saying in a local television address.
Abdullah met with Manmohan Singh, the Indian prime minister, and attended a meeting with the government's security cabinet in New Delhi on Monday to discuss the crisis.
The recent unrest in the disputed territory, the worst spate of violence in two years, began when a 17-year-old student was killed by a police tear-gas shell in early June.
Indian security forces, so far, have been accused of killing 25 civilians in less than two months.
Both Pakistan and India control part of the disputed Kashmir region. But each side lays claim over the whole of the territory.
Separatist politicians and fighters reject Indian sovereignty over Kashmir and want to carve out a separate homeland or merge with neighbouring predominantly-Muslim Pakistan.
The Himalayan region has been in upheaval since the early 1990s in a separatist insurgency that has claimed thousands of lives.