Prime Minister Manmohan Singh has told Indians celebrating 60 years of independence from Britain that "the best is yet to come".
Mr Singh was speaking after raising the Indian flag at Delhi's Red Fort, where the British flag was lowered in 1947.
He praised the work of those who fought for India's freedom but said the country would only be truly independent once it had eliminated poverty.
Pakistan marked its own 60th anniversary a day earlier.
The partition in 1947 saw 10 million people cross borders in one of history's largest mass migrations.
But freedom for both countries came at a price as hundreds of thousands of people died in the violence that followed.
India looks to future
A military band fired guns and played the national anthem as the Indian flag was raised at the historic Red Fort in the centre of the capital.
Hundreds of balloons in the colours of the Indian flag were released into the air.
Amid tight security, Mr Singh said: "I assure you that for each one of you, and for our country, the best is yet to come."
But he also said too few Indians enjoyed the benefits of one of the fastest growing economies in the world.
"Sixty years ago we started a new journey. We were inspired by Mahatma Gandhi's thoughts and views. In the true sense we will have freedom and independence only when we get rid of poverty."
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He urged the nation to work hard to "eradicate malnutrition within five years".
Mr Singh pledged to press ahead with industrialisation and improving infrastructure but there was no mention of the other nation created at the time of the bloody partition - Pakistan.
The BBC's Sanjoy Majumder, in Delhi, says there is clear concern among India's leaders that the benefits of its booming economy have not reached a vast majority of its one-billion strong population.
But despite this, the mood in India is upbeat, with many believing that the country has finally emerged out of its colonial shadow to take its position on the global stage, our correspondent adds.
Major security drive
Earlier, thousands of people attended a huge concert at Wagah, where the only road border between India and Pakistan is found.
The BBC's Alastair Leithead, at Wagah, says there was a sense from people there that they would like to see the community spirit that was alive when this was one country to be born again.
As celebrations got under way across India, a huge security operation swung into action to thwart possible militant attacks.
Aircraft and tens of thousands of security forces have been deployed to fend off what the government says are threats by al-Qaeda and insurgents in several states.
In Delhi, around 70,000 policemen and paramilitary troops were posted at government buildings, diplomatic enclaves and main intersections.
Four explosions rocked the north-eastern state of Assam hours before the celebrations began.
No-one was killed or injured in the blasts. The police blamed the explosions on the separatist United Liberation Front of Assam (Ulfa) rebels, who have called for a boycott of the celebrations.
Separatist groups in Indian-administered Kashmir said that the celebrations were a "Black Day".
A strike sponsored by the groups closed shops and businesses there.
Jammu and Kashmir Chief Minister Ghulam Nabi Azad spoke at a ceremony from behind a bullet-proof screen, urging militants to turn to "peace and prosperity".
In some rural areas in eastern India, Maoist militants raised black flags to protest against the celebrations.
The festivities were also muted in many areas of northern India where millions have been affected by some of the worst flooding in 30 years.
To herald the celebrations in both countries, Pakistan allowed 134 Indian prisoners to return home on Monday, with India reciprocating by handing over 72 Pakistani prisoners on Tuesday.