Here are the top 10 tasks that kept the PM busy on Day 1:
Mr Modi, known to be an early riser, reached his office at the South Block at 9 am. After stepping into the Prime Minister's office for the first time, he offered flowers to a Mahatma Gandhi picture.
The social media-savvy prime minister's first tweet of the day was a tribute to India's first Prime Minister Jawaharlal Nehru, who died on this day, 50 years ago.
Mr Modi then held a series of meetings with the heads of state of South Asian Association for Regional Cooperation, or SAARC, nations. These leaders had attended the grand swearing-in ceremony at the Rashtrapati Bhavan - one of the biggest events held at the Presidential Palace -- on Mr Modi's invitation.
Among the leaders Mr Modi held bilateral meetings were Afghanistan President Hamid Karzai, Maldives President Yameen Gayoom, Sri Lanka's Mahinda Rajapaksa, Bhutan Prime Minister Tshering Tobgay, Mauritius PM Navin Ramgoolam, Nepal Prime Minister Sushil Koirala and Bangladesh Speaker Shirin Chaudhury.
But Mr Modi's most crucial engagement of the day was the bilateral meeting he held with Pakistan Prime Minister Nawaz Sharif at around 12.45 pm. Incidentally, Mr Sharif was the first to shake hands with the new prime minister after the swearing-in ceremony.
During the meeting, Mr Modi, whose BJP has traditionally maintained a strong stance towards Pakistan, raised the issue of cross-border terror. The prime minister also brought up the slow pace of the 26/11 trial in Pakistan and the recent attack on the Indian Consulate in Herat, Afghanistan. The meeting lasted for 45 minutes.
In what was reportedly his "first decision" after taking over, the PM also announced a relief of Rs. two lakh each for the families of those killed and Rs. 50,000 for those seriously injured in yesterday's train accident in Uttar Pradesh.
Mr Modi also called on his predecessor Manmohan Singh, whom he has often attacked for being 'too soft' in the past. The meeting has been described as a "courtesy call".
The Prime Minister is holding a meeting with his Council of Ministers. After wide-spread speculation about who will get which ministry, and some embarrassing moments for soon-to-be ministers who inadvertently leaked their portfolios, the official list was released today morning.
Mr Modi also met senior officials of his government.