Modi quoted a poem by Vajpayee to express his feelings. It spoke of Vajpayee's lack of fear of death.
"Atalji is not with us now but every Indian and every BJP worker will get inspiration and guidance from him. May the Almighty rest his soul rest in peace and give strength to everyone who loved him to bear the loss. Om Shanti," he said.
Vajpayee, a founder-member of the BJP and the first non-Congress Prime Minister to complete a full term in office, died in after prolonged illness. Vajpayee, a bachelor, is survived by his adopted daughter, Namita Kaul Bhattacharya.
His death was announced by the All India Institute of Medical Sciences (AIIMS) hospital, where he was admitted on June 11 with a variety of ailments.
Vajpayee’s body will be taken to his residence in the national
capital where people can pay their last respects, Home Minister Rajnath Singh said.
Singh, who visited the AIIMS twice during the day when Vajpayee was on life support, said the nation lost a stalwart who had dreamt of an India where "all persons lived together in unity, peace and harmony".
"In Atalji's demise the nation has lost a stalwart who was known for statesmanship and astute leadership. Atalji was a true 'Ajatshatru' (man with no enemies) who had many friends across the political spectrum. He believed in political consensus and his beliefs had consequential effect on Indian politics," he said.
"I cannot fully imagine my own life without following the footprints that Atalji set. May his soul rest in peace," he said.
BJP President Amit Shah said Vajpayee nursed the party to make it a banyan tree and left an indelible mark in Indian politics.
"Atalji emerged as a popular national
leader who believed that power is a means of service and led a spotless political life without compromising on national
interest. And that's why the people across political and social boundaries showered him with love and respect," Shah tweeted.
"A rare politician, brilliant speaker, poet and patriot, his demise is not just a irreparable loss for the BJP but also for the entire country," the BJP chief said.
"On the one hand Atalji as the head of a party in opposition played the role of an ideal opposition while on the other hand he provided the country a decisive leadership as Prime Minister," Shah said.
President Ram Nath Kovind said Vajpayee, a "gentle giant", will be missed by all. In a Twitter post, Kovind said the late leader’s foresight, maturity and eloquence put him in a league of his own.
"Extremely sad to hear of the passing of Shri Atal Bihari Vajpayee, our former prime minister and a true Indian statesman," he said.
Former President Pranab Mukherjee tweeted: "Deeply saddened at the passing away of Shri Atal Bihari Vajpayee. A reasoned critique in opposition and a seeker of consensus as PM, Atal Ji was a democrat to the core. In his passing away, India has lost a great son and an era has come to an end. My deepest condolences."
Veteran BJP leader L K Advani, who along with Vajpayee was a central figure in the party for much of its existence, described the former prime minister as one of the country's tallest statesmen and his closest friend for over 65 years whom he will miss immensely.
Leaders of the opposition camp too paid tributes to the late politician.
Congress president Rahul Gandhi said India lost a great son who was loved and respected by millions.
"Today India lost a great son. Former PM, Atal Bihari Vajpayee ji, was loved and respected by millions. My condolences to his family and all his admirers. We will miss him," he said on Twitter.
West Bengal Chief Minister Mamata Banerjee tweeted: “Very very saddened that the great statesman and former PM Shri Atal Bihari Vajpayee ji is no more with us. His passing away is a very big loss to our nation. I will always cherish the many fond memories. Condolences to his family and his many admirers.”
Delhi Chief Minister Arvind Kejriwal, who visited AIIMS, posted on Twitter: "Am deeply saddened. A great loss for India.”