Manmohan Singh is beginning an official visit to Burma, the first by an Indian prime minister since 1987.
Singh said he hoped to strengthen trade and diplomatic co-operation during his three-day trip.
He will meet President Thein Sein and opposition leader Aung San Suu Kyi, whose mother once served as Burma's ambassador to India.
The two nations share a 1,600km border, but relations have often been uneasy.
The Delhi government cold-shouldered Burma's military rulers during the 1990s, infuriating the generals by openly supporting Suu Kyi.
India has already signed a number of deals for the exploitation of Burma's vast reserves of natural gas, and Indian firms are building ports and other infrastructure projects in Burma.