Modi marked the occasion by asking Indians to set aside their differences to help rid the country of long-standing social ills such as class prejudice and corruption.
"India is about peace, unity and goodwill," said Modi. "We have to take the country ahead with the determination of creating a new India."
In Modi's new India, the country's youthful population will keep up with changes in the global economy, villages will have electricity and "the poor will have concrete houses with water," said the Prime Minister, referring to some of his administration's major projects in the last three years.
In a speech heavy with symbolism, Modi outlined a vision of an inclusive and unified India in which "there is no one big or small ... everybody is equal."
"Together, we will make an India free of terrorism, communalism and casteism. Together we will make an India free of corruption and agreements based on nepotism. Together we will make an India that is clean, healthy and self-reliant," said Modi.
Yet distance remains between the dream and the reality. The Prime Minister started his speech by paying tribute to the more than 60 children
who died this month while receiving care at a governmental medical college in India's biggest state.
While the cause of death is under dispute, allegations of negligence and corruption surround the incident.
Mob violence directed against India's religious minorities
and lower castes have forced Modi to speak out explicitly against sectarian divisions between Hindus and Muslims in recent months.
On Tuesday, he reiterated previous calls to end partisan violence
. "There can be no room for divisions. We have to move forwards together. Casteism and communalism will not help us."
The celebrations started with Modi's arrival at Red Fort, where he was greeted by a contingent of military and police personnel, as well as 8,500 schoolchildren, who had been assembled in formation to spell out the word "Bharat" or "India" in Hindi.
The army members had been specially selected from a battalion force in Indian-administered Kashmir. In the wake of partition, India and Pakistan's bloody division, volunteers had come together to form this battalion known as the 8th Jammu & Kashmir Light Infantry.
After Modi descended from the podium he was overwhelmed by schoolchildren eager to say hello and to get their photo taken.
Outside, thousands of people braved the heat, hoping to get a photo. As the speech ended, orange, white and green balloons were released into the sky.
The partition of India and Pakistan ended two centuries of British colonial rule and saw one of the largest human migrations the world has ever seen.
The border, cutting through Bengal in the east and Punjab in the west, was confirmed two days after India became independent. A line was quickly marked on maps using censuses of "minority" and "majority" populations.
An estimated 12 million-15 million people left their homes and crossed the new border based on their faith -- Muslims to Pakistan, while Hindus and Sikhs took the opposite journey.
At least 1 million people died in communal attacks as they crossed the border and tens of thousands of women and girls were abducted and raped.
This hastily drawn line and the violence that followed continues to plague ties between India and Pakistan to this day.
The two nations have fought four wars since 1947, mostly due to disputes over the northern Himalayan state of Jammu and Kashmir.
Attempts to renew dialogue and restore peace have been made numerous times, but for now relations between the nuclear-armed neighbors remain hostile.