Mr Modi also paid tributes to those who died of the virus, saying "the pain of losing them will stay with us forever".
He added that the country fought the virus "with extraordinary pace".
But his government faced criticism when India's second Covid wave ravaged many towns and cities in April and May, reports the BBC.
The second wave left millions of people infected and overwhelmed the country's fragile healthcare system to the point of collapse.
People died gasping for breath as hospitals ran out of beds and oxygen - leaving distraught family members pleading for help on social media. Even crematoriums in some cities ran out of space.
Daily case counts have since fallen sharply from a high of 400,000 at the peak of the crisis to around 30,000 to 40,000. But there is a looming fear of a third wave as millions of Indians are still vulnerable.
In his speech from Delhi's historic Red Fort complex on Sunday, Mr Modi also praised India's vaccination programme, saying more than 500 million people in India had received at least one dose. But so far only 12 per cent of the population has been fully vaccinated in India.
The government aims to vaccinate all adults by the end of this year, but the drive has been hobbled by slow pace, shortage of doses and vaccine hesitancy.
Apart from focusing on Covid, Mr Modi also spoke about India's historic performance at the Tokyo Games, the country's development goals, the economy and climate change.
Here are the key takeaways from his speech:
Glory in Tokyo
Mr Modi started this year's ceremony by honouring India's Olympics contingent.
India recorded its best-ever showing at Tokyo this year by winning seven medals - one gold, two silver and three bronze - surpassing the six it won in London in 2012. Many of the medal winners were invited as special guests at the ceremony on Sunday.
"These players have not just won all our hearts but have set an example for future generations," Mr Modi said.
Economy
Mr Modi also spoke about his vision for India's development, saying the next 25 years will mark the country's growth story.
He talked about boosting manufacturing and exports, encouraging home-grown industries and promoting innovation. For this, the prime minister said, the government would launch an infrastructure plan worth $13.5m (£9.7m).
The aim, Mr Modi said, was to ensure that the benefits of the economy should trickle down to every village and town in India.
But his promises come at a time when the Indian economy is struggling to recover from the damage caused by coronavirus. Growth had been faltering even before 2020 and the pandemic has made matters worse.
The virus has left deep scars - unemployment is on the rise while inflation remains high. India's GDP shrunk by an unprecedented 7.3 per cenr in the previous financial year as the pandemic wiped out businesses.
The government has repeatedly spoken of achieving a sharp recovery in the coming months. But several financial institutions, including the World Bank and the International Monetary Fund, have revised expectations downwards.
Farmers
In recent days, Mr Modi's biggest challenge has been to tackle the growing discontent among India's farmers who are angry with a set of new laws aimed at reshaping the country's agriculture industry.
It wasn't surprising that he referred to the community several times in his speech, saying his government aims to make small farmers - who own less than two hectares of land - "the pride of India".
"In the coming years, we will have to increase the collective power of the small farmers of the country. We have to give them new facilities. They must become the country's pride," Mr Modi said.
His comments came as tens of thousands of farmers continue to camp out on the outskirts of Delhi to protest against the new farm laws.
Partition
Mr Modi also announced that India will mark 14 August every year as "Partition Horrors Remembrance Day". He said the decision was taken to honour those who died in the bloodied partition of India in 1947.
But his critics say that marking the day will only open painful memories for many.
India celebrates its Independence Day a day after its neighbour Pakistan. Two newly-independent states were created after the partition of British India in 1947. The process triggered one of the largest migrations in human history as millions of people fled their homes and tens of thousands died.
Climate change
The prime minister talked about the importance of handling climate change, adding that India was committed to meet its target of reducing its carbon footprints.
He announced that his government would invest more in greener sources of energy. He particularly talked about increasing investments in solar energy.
