Mr Vajpayee was one of India's most charismatic leaders and inspirational orators.
Leaders from across the world including US and Russia have expressed grief over the death of former prime minister Atal Bihari Vajpayee and recalled his contributions in strengthening bilateral relations and maintaining regional peace.
Russian President Vladimir Putin sent a message of condolences to President Ram Nath Kovind and Prime Minister Narendra Modi on the demise of Vajpayee. Mr Putin referred to the former prime minister as "outstanding statesman".
"Atal Bihari Vajpayee rightly commanded great respect around the world. He will be remembered as a politician who made a major personal contribution to the friendly relations and privileged strategic partnership between our countries.The President of Russia conveyed words of sincere sympathy and support to the family of the deceased, the Government and the people of India," the message read.
US Secretary of State Michael Pompeo said Mr Vajpayee recognised early on that the US-India partnership would contribute to the world's economic prosperity and security and the two democracies continue to benefit from his vision.
"On behalf of the people of the United States of America, I extend my heartfelt condolences to the people of India on the recent passing of former prime minister Atal Bihari Vajpayee," Mr Pompeo said in a statement yesterday.
He recalled Mr Vajpayee's address to the Congress in 2000, when he had famously characterised US-India ties as a "natural partnership of shared endeavours".
"Today, our two countries and our bilateral relationship continue to benefit from Prime Minister Vajpayee's vision, which helped promote expanded cooperation," Mike Pompeo said.
He said the American people stand with the people of India "as we mourn Prime Minister Vajpayee's passing".
Nepal Prime Minister KP Sharma Oli took to Twitter to express his grief and said: "I am deeply saddened to learn of the passing away of Shri Atal Bihari Vajpayee, former Prime Minister of India. May the departed soul rest in eternal peace!"
In his message to PM Modi, Mr Oli said: "Late Vajpayee was a visionary statesman with impeccable integrity and dedication. He will be remembered for his sagacity and exemplary selfless service to the people of India.
"In his demise, India and the world lost a towering political figure and Nepal a true friend and well-wisher. His contribution to strengthening Nepal-India relations will be remembered forever".
May the departed soul rest in eternal peace! Mr Oli said.
Sri Lankan President Maithripala Sirisena and Prime Minister Ranil Wickremesinghe have condoled the death of Mr Vajpayee and said he played a vital role in ensuring stability of the island nation.
Bangladesh Prime Minister Sheikh Hasina has expressed "deep shock" at Mr Vajpayee's death and said he was "our great friend and highly respected" in the country.
Pakistan government and top leaders including Prime Minister-in-waiting Imran Khan and PML-N chief Shahbaz Sharif have paid respects to Mr Vajpayee and said he contributed to bringing "a change" in bilateral ties and remained a key supporter of regional cooperation for development.
"Mr Vajpayee was a renowned statesman who contributed to bringing a change in India-Pakistan relations and remained a key supporter of SAARC and regional cooperation for development," the Foreign Office said in a statement.
Maldives President Abdulla Yameen Abdul Gayoom has sent a message of sympathy and condolences to President Ram Nath Kovind following the demise of Vajpayee.
"It was with deep sorrow that I learned of the demise of Former Prime Minister of India, Mr. Atal Bihari Vajpayee, who would not only be remembered for his distinguished service and leadership for his country but also as a scholar who has made immense contribution to literature and art.
"We would fondly remember the Former Prime Minister Vajpayee for his contribution to human resource development in the Maldives, and for the memorable visit that he made to the Maldives during his tenure as the Prime Minister of India," he said in the message.
"At this time of national loss, the Government and the people of the Maldives joins me in extending our profound sympathy to Your Excellency, the government and the people of India," the message reads.
Mauritius Prime Minister Pravind Kumar Jugnauth conveyed his condolences in a letter addressed to PM Modi.
"Shri Vajpayee shaped the destiny of India through his bold leadership and his deep rooted empathy for the common man...," the message reads.
The Government of Mauritius has decided that both Indian and Mauritian flag will fly half-mast on government buildings today as a mark of respect following the demise of Mr Vajpayee.
Israeli Ministry of Foreign Affairs' Director General Yuval Rotem said he was "deeply saddened to learn of the death of a giant - India's former prime minister Atal Bihari Vajpayee".
"I offer my heartfelt condolences to the people of India at their loss," he said in a tweet which also features a picture of Mr Vajpayee shaking hands with former Israeli prime minister Ariel Sharon.
Bhutan's former prime minister Tshering Tobgay said in a tweet: "Heartfelt condolences to the Government and people of India on the passing of #AtalBihariVajpayee. The world will celebrate him as an exemplary statesman."
Mr Vajpayee, one of India's most charismatic leaders and inspirational orators, died on Thursday at the age of 93 in New Delhi.