"If this issue of terrorism is not addressed, all good intentions that we have for our two peoples to live in peace and harmony will be negated," he said.
Touching on the Kashmir violence, Singh used his speech to attack those intent on "dividing people in the name of religion" - an apparent reference to both Hindu and Muslim hardliners.
New Delhi, the Indian capital, was turned into a fortress on Friday as sandbag defences were placed at key intersections and a two-hour no-fly zone was enforced for the main celebrations.
Police barricaded New Delhi's 18 entry points from adjoining states and said that the city borders would remain sealed during the celebrations, held every year to mark the end of British colonial rule in 1947.
Officials said the tight security was prompted by "inputs" of possible attacks during the celebrations.
Security was also at its peak in Indian Kashmir, which remains engulfed in deadly protests over a land row that has inflamed religious tensions and stoked a separatist campaign in the Himalayan territory.
In Mumbai, India's financial hub, was also put on high alert. Police searched the city for suspects as a precaution after serial blasts rocked the nearby city of Ahmedabad last month. At least 70 people were killed and 170 others injured in the blasts.