Speaking at the National Integration Council, Chidambaram said: "The biggest challenge is the use of violence as an instrument of protest or an instrument of change. Insurgency, militancy and terrorism threaten to unravel the idea of India."
He also said the country still faces the old evils like communalism, casteism and parochialism.
Chidambaram said it was natural to focus on violent attacks of terrorist groups but attention must be given to the violence unleashed by ideologically-driven Left wing extremists and recalcitrant separatist groups in northeastern states.
The NIC, which is meeting after three years, is discussing the communal violence bill.
The other issues are radicalisation of youth in the name of religion and how caste emboldens them to take to the path of violence.
"I would like to ask this council to guide us on how to deal with the issues that are included in the agenda.
"In particular, I would like to ask you whether the institutions that we have - of both government and civil society - are adequate to meet these grave challenges and, if they are not, how do we strengthen these institutions or set up new institutions," Chidambaram said.
Chief Minister of Gujarat Narendra Modi, Bihar Chief Minister Nitish Kumar, Tamil Nadu Chief Minister J.Jayalalithaa and Uttar Pradesh Chief Minister Mayawati were among those who were not present at the meeting.
West Bengal Chief Minister Mamata Banerjee sent her representative Amit Mitra, the finance minister of the state - for the meet.