At least 57 people have died in clashes between protesters and security forces in the latest phase of protests since June.
Protesters have been defying almost daily curfews imposed by the government over the past two months.
Security was tight in Kashmir for India's 63rd independence day celebrations, but thousands took to the streets defying a strict curfew.
The impasse in Kashmir found a mention in the speech that the Indian prime minister delivered in New Delhi on the occasion.
Manmohan Singh called for an end to violence by separatists in Kashmir and by Maoists in other parts of the country.
"The years of violence should now end. Such violence would not benefit anyone."
"I believe that India's democracy has the generosity and flexibility to be able to address the concerns of any area or group in the country."
Dialogue with Pakistan
Singh also said that a dialogue with Pakistan would go nowhere unless Islamabad cracks down on those launching attacks against India from its territory.
"As far as Pakistan is concerned, we expect from them that they would not let their territory be used for acts of terrorism against India," Singh said.
"If this is not done, we cannot progress far in our dialogue with Pakistan."
India suspended a peace dialogue with Pakistan in the wake of the November 2008 Mumbai attacks, which claimed 166 lives.
India accuses the Lashkar-e-Taiba, a group based in Pakistan, for the Mumbai carnage.
The two countries have only recently resumed structured talks.