Those who enquired after included prime minister Narendra Modi, union ministers and Bharatiya Janata Party (BJP) stalwarts.
Vajpayee was admitted to hospital on June 11 with a kidney tract infection and chest congestion.
Indian politicians and celebrities, including cricket captain Virat Kohli and opposition Congress party leader Rahul Gandhi, took to Twitter to post their condolences.
In keeping with the military honours, three service chiefs placed wreaths on the body of Vajpayee before leaders paid their floral tributes.
People pay tribute to former prime minister Atal Bihari Vajpayee in Lucknow.
The country observed a seven-day state mourning as a mark of respect for the leader. Vajpayee was undergoing a treatment at All India Institute of Medical Sciences (AIIMS) for the past 9 weeks.
The South Asian Association for Regional Cooperation (SAARC) on Friday condoled Vajpayee's death, describing him as a strong advocate of cooperation within the South Asian region.
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This was a silent gesture of PM Modi to show how much he loved and respected BJP stalwart AB Vajpayee.
"Sub-continent has lost a phenomenal and a visionary political figure today", the Pakistan Tehreek-e-Insaf (PTI) chairman said in a statement.
"Vajpayee, as foreign minister, took responsibility of improving India-Pakistan ties", Khan was quoted as saying.
Describing former prime minister's death as a "huge personal loss", Singh said he was pained beyond words at the demise of Vajpayee, who had cherished the ideal of a developed and powerful India.
"France offers its condolences to his family as well as the Indian authorities and people", it said. "His name remains linked to the Indo-French friendship, which he shaped by launching the strategic partnership that has united our two countries since 1998".
The flag will fly at half mast and Vajpayee will be accorded a state funeral, the government has also decided. Khan said, "I extend sympathies to the people of India in this hour of grief".
Vajpayee was the prime minister between 1998 and 2004 when the National Democratic Alliance government was in power.
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