This handout photograph taken on June 20, 2023 and released by the Indian Press Information Bureau (PIB) shows India s Prime Minister Narendra (R) and SpaceX, Twitter and electric car maker Tesla CEO Elon Musk during their meeting in New York. AFP
Musk, one of the world's richest men, said that Modi was "pushing us to make significant investments in India, which is something that we intend to do, and are trying to figure out the right timing".
New Delhi has rolled out the red carpet for top global investors and companies -- including tech giants like Google and Apple -- in the last few years.
Since the coronavirus pandemic, many companies have expanded their presence in India as a way to cut their supply-chain dependence on China and tap into the South Asian nation's huge domestic market.
Modi, who saw the tech billionaire shortly after arriving from India on a state visit, said it had been "great meeting" Musk in New York.
"We had multifaceted conversations on issues ranging from energy to spirituality," Modi tweeted on Wednesday, a day before he is due to be hosted by US President Joe Biden for a state dinner.
Musk said he was a "fan" of Modi.
"I am actually incredibly excited about the future of India. India has more promise than any large country in the world," he added.
Musk has faced questions from free speech activists over Twitter reportedly caving into the Indian government's demands for takedowns of critical posts.
Critics accuse India's government of democratically backsliding, including by curtailing free speech and not doing enough to check attacks on journalists and minorities.
Last week, former Twitter chief executive Jack Dorsey said the platform he founded had come under sustained pressure from Indian officials during his tenure.
Indian information technology minister Rajeev Chandrasekhar responded that Dorsey's claim was an "outright lie", while also accusing Twitter of repeated violations of local laws.
Twitter said last year that India ranked fourth globally in the number of requests made by a government to remove content -- behind Japan, Russia and Turkey.