In a speech in Delhi, Mr Modi accused Kashmiri separatists of "scheming".
Muslim-majority Kashmir is at the centre of a decades-old territorial dispute between India and Pakistan.
Mr Modi said only "hugs" could solve the problems of the territory, which often sees clashes between protesters and Indian security forces.
India is celebrating its 70th Independence Day a day after its neighbour Pakistan.
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Mr Modi urged Indians to stand together with Kashmiris to rediscover "the lost paradise".
He also appealed to the nation to stand together with the families of 60 children who died at a public hospital in northern India after oxygen supply was cut over unpaid bills.
The prime minister also spoke in support of Muslim women who are fighting a legal battle to abolish the practice of "triple talaq" (instant divorce).
India is one of a handful of countries where a Muslim man can divorce his wife in minutes by saying the word talaq (divorce) three times.
India's Supreme Court is soon due to give a ruling in the case.
Mr Modi also criticised people for using religion to incite violence.
Vigilantes who portray themselves as protectors of cows - an animal considered sacred by Hindus - have been frequently attacking people suspected of smuggling the animal since Mr Modi's Bharatiya Janata Party came to power in 2014.
The slaughter of cows is banned in several Indian states.
Nearly a dozen people have been killed in the past two years in the name of the cow. Targets are often picked based on unsubstantiated rumours and Muslims have been attacked for even transporting cows for milk.
Indian Prime Minister Narendra Modi has said that "bullets and abuses" cannot bring peace in Kashmir, as the country celebrates 70 years since independence.