"He was a simple but matured politician who played a leading role in the peace process between the two countries," Information Minister Sheikh Rashid told AFP.
"It is sad news. I must say that the peace process has slowed down after Vajpayee," he added.
The 81-year-old Vajpayee told a public rally in Mumbai this week that he would not contest his seat at future elections. He stepped down as prime minister last May after his Bhartiya Janata Party suffered a stunning defeat at the hands of the Congress party in national elections.
He was instrumental in starting peace moves with Pakistan in January 2004, less than two years after the long-term rivals came to the brink of a fourth war.