In his message, Bainimarama underscored Fiji's political, economic and cultural cooperation as well as strategic alliance with India, Xinhua reported.
"On behalf of the government and the people of Fiji, my profound congratulations to your excellency on your momentous election victory and your appointment as prime minister-elect of the government of India. The elections that have just taken place are model of the exceptional robustness of Indian democracy," Bainimarama said in a statement.
"Your democracy, the world's largest, stands witness to India's deep commitment to the secular values to which my government feels particularly attached, " Bainimarama said.
Bainimarama said that Fiji looks forward to strengthening current relations for the development of the two nations.
"I take this opportunity to extend a warm and cordial invitation to you to visit Fiji at a time of convenience to you," Bainimarama added.