He was also one of the founding members of the Hindu nationalist Bharatiya Janata Party (BJP), which now governs India.
Mr Vajpayee, the BJP's tallest leader, was admitted to hospital on June 11 with a kidney tract infection and chest congestion.
In keeping with the military honours, three service chiefs placed wreaths on the body of Vajpayee before leaders paid their floral tributes.
"He will be remembered as a politician who made a great personal contribution to the development of friendly relations between our countries and the development of Russian-Indian highly privileged strategic partnership", the Russian leader said in a letter to Prime Minister Narendra Modi.
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The city urges residents to survey their own property to ensure any potential breeding areas are properly maintained. During all of 2017, there was one human case reported while the total number of ZIP Codes testing positive was four.
State mourning for seven days till 22 August.
Vajpayee, who passed away at AIIMS on Thursday evening, had a pan-India appeal and his flair for foreign policy and initiatives were acknowledged globally.
In his death too, the charismatic Atal Bihari Vajpayee managed to bring political opponents together. Khan said in a statement that Vajpayee was a prominent political personality of the sub-continent and his death has created a big void.
The SAARC secretary general also recalled Vajpayee's "grand diplomatic gesture" of taking bus rides to Lahore and Dhaka during his prime ministership. My condolences to his family & all his admirers.
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Using the N-word wasn't just the way he talks but, more disturbing, it was how he thought of me and African-Americans as a whole'. Manigault Newman also alleges that allies of the president tried to buy her silence. "I didn't want to believe it", she writes.
"He was a charismatic politician who took pride in India and took everyone along. 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". ALSO READ: Atal Bihari Vajpayee, more than a rare "Ajatshatru" in Indian politics Other attendees of the funeral included Home Minister Rajnath Singh, Union ministers Harsh Vardhan, Ram Vilas Paswan, Shripad Naik and Piyush Goval. "I wanted to pay my respects to a man of that stature".
The Dalai Lama, the Tibetan spiritual leader, sent a condolence message to Vajpayee's foster daughter, Namita Bhattacharya, saying India had lost an eminent national leader who had eloquently supported the Tibetan people.
Khan said that Vajpayee started efforts for improving Indo-Pak ties and continued them after becoming prime minister.
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