India declared a day of mourning across the country on Saturday, with the national flag to be flown at half-mast and no official entertainment.
Mr Modi was joined by other senior Indian figures in paying tribute to a “great statesman”.
“I am deeply saddened to know about the passing away of HH Sheikh Khalifa bin Zayed. He was a great statesman and visionary leader under whom India-UAE relations prospered. The heartfelt condolences of the people of India are with the people of UAE. May his soul rest in peace,” Mr Modi said in a statement.
Dr Subrahmanyam Jaishankar, India's External Affairs Minister, said Sheikh Khalifa will be remembered as a “leader who modernised and empowered the United Arab Emirates”.
Pinarayi Vijayan, the chief minister of India’s southern Kerala state, also offered his condolences.
Sheikh Khalifa, who served as the president of the UAE and ruler of Abu Dhabi since November 2004, died at the age of 73 on Friday, the state news agency WAM reported.
Mr Vijayan called the deceased leader a visionary as he hailed his “cordial relations with Kerala” — a region that sends the highest number of immigrants to the Gulf nation.
“Deeply saddened by the passing of the UAE President His Highness Sheikh Khalifa bin Zayed Al Nahyan who has always kept cordial relations with Kerala. He was a visionary leader who played a key role in modernising the Emirates. His contributions will be remembered forever,” he said.
The UAE's Ministry of Presidential Affairs has announced a 40-day period of official mourning, with flags flying at half-mast.
Condolence messages also poured in from other Indian politicians.
India’s Commerce Minister Piyush Goyal called the late president a reformer and praised him for fostering deeper relations between India and the UAE.
“A strong and visionary leader, he steered the UAE through path-breaking reforms making it an oasis of prosperity. His contribution in fostering deeper India-UAE ties cannot be overstated,” Mr Goyal wrote on Twittter.