Vajpayee, a risk-taker Photograph:( Reuters )
The translated version of Li's letter to PM Modi was tweeted by the Indian Embassy.
Chinese Premier Li Keqiang described former Prime Minister Atal Bihari Vajpayee as an "outstanding politician".
Keqiang noted that Vajpayee was a leader who made a significant contribution to the development of the Sino-Indian relations.
He added that he was deeply "saddened to learn the passing away of AB Vajpayee, former Prime Minister of India," read Keqiang's letter to Prime Minister Narendra Modi.
The translated version of Keqiang's letter to PM Modi was tweeted by the Indian Embassy.
"On behalf of the Chinese government and its people, I would like to extend my deep condolences and express my sincere sympathy to the bereaved family," he said.
"Vajpayee was an outstanding politician who devoted his life for national and social development and had earned widespread respect among the Indian people," the Chinese premier added.
In his letter, Keqiang described the importance of China-India relations and stated that his country would like to work together with India to push forward bilateral ties.
Former Prime Minister Atal Bihari Vajpayee, during his tenure, had visited China in the year 2003, the same year the two countries set up the Special Representatives mechanism to resolve the boundary dispute.
Keqiang added that under Vajpayee's rule Indo-China ties made great strides.
Former PM and Bharat Ratna Atal Bihari Vajpayee breathed his last on August 16 at Delhi's All India Institute of Medical Science. He was 93.
According to the official statement released by AIIMS, Vajpayee passed away at 5.05pm. He was cremated with full state honours at Smriti Sthal in Delhi on August 17.