Namita Kaul Bhattacharya, adopted daughter, and Niharika Bhattacharya, grand daughter, pay tribute to former prime minister Atal Bihari Vajpayee, at his Krishna Menon Marg residence, in New Delhi.
He was being treated for a kidney tract infection, urinary tract infection, low urine output and chest congestion.
"Prime Minister Vajpayee's efforts towards establishing an atmosphere of trust between India and Pakistan will be his lasting legacy,"Bilawal said, hoping that India's current leadership exhibits similar intentions and commitment towards sustainable peace in South Asia".
Vajpayee, a Hindu nationalist from the Bharatiya Janata Party, ordered nuclear weapons tests in 1988 that stoked fears of atomic war with rival Pakistan.
He first became PM of India for only 16 days - May 16-31, 1996, and was re-elected PM in March 1998, where he remained in office until May 13, 2004.
"As foreign minister Vajpayee strived to open up ways towards normalisation of relations among neighbouring states and had successfully taken this agenda to new heights after assuming office of the prime minister", the statement read.
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Atal Bihari Vajpayee was one of the founding members of the Hindu nationalist Bharatiya Janata Party (BJP), which now governs India.
But the next year, when Islamabad sent fighters across the cease-fire line that divides the disputed Himalayan region of Kashmir between the nations, Vajpayee resisted military pressure to launch a broad counter-attack of Indian forces.
Atal Bihari Vajpayee, a diabetes patient, was admitted to AIIMS on June 11 for what doctors had described as a routine check-up. He further said that Indians will reflect on Vajpayee's many contributions that led to the country's rise as a global and economic power.
Rahul Gandhi, the leader of the Congress party, said "India has lost a great son" who was "loved and respected by millions".
"It was Atal Ji's exemplary leadership that set the foundations for a strong, prosperous and inclusive India in the 21st century", Mr Modi said in a tweet. "He will be remembered for his enormous contribution in bolstering US-India relations". The Modi government in 2014 that Vajpayee's birthday, December 25, would be marked as Good Governance Day.