Kumar in a series of tweets also shared pictures of meeting of Swaraj with other leaders separately, including Bangladesh Foreign Minister Abul Hassan Mahmud Ali and Acting Foreign Minister of Sri Lanka Lakshman Kiriella. Former Afghan president Hamid Karzai was also among the mourners.
"Leader who was respected deeply for his humility!"
"Former PM, Atal Bihari Vajpayee was loved and respected by millions".
Mr Vajpayee was one of the most popular leaders of Prime Minister Narendra Modi's ruling Hindu nationalist Bharatiya Janata Party (BJP).
The government and people of Pakistan extend their "heartfelt condolences" to Vajpayee's family and to the government and people of India, the spokesman said.
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Sial, who is from Pakistan and assumed office as SAARC secretary general in March 2017, recalled Vajpayee's statements at the 10th SAARC Summit in Colombo in 1998, in Kathmandu in 2002 and in Islamabad in 2004 and said: "His vision for a self-reliant and fully integrated South Asia continues to guide the Saarc process even today".
A government spokesperson said Chief Minister Yogi Adityanath has ordered immersion of Vajpayee's ashes in every district as Uttar Pradesh was his "karma bhumi" and every region of the state had a close link with him.
"It was with deep grief that we learnt of the demise of former Indian Prime Minister Atal Bihari Vajpayee", the French foreign ministry said in a statement.
Modi said Vajpayee's stewardship had put India on a fast track to growth. In 2000, then Home minister L.K. Advani visited Israel - becoming the most senior representative from India to visit the country. Meanwhile, the British High Commission in Delhi flew its national flag, the Union Jack, at half mast in honour of Vajpayee.
Pakistan's government also paid tribute to Vajpayee. "The upswing in India-Japan relations was only possible by the initiatives started by Prime Minister Vajpayee", Hiramatsu said. "Deepest condolences conveyed by our friends from Nepal on the loss of a visionary leader! May his legacy live on, and may his soul rest in eternal peace", he added.