"China will, as it has been doing, pay great importance to developing relations with India and expects to carry out close cooperation with India to create a brighter future of their of their bilateral relations," Xi wrote in a letter to Singh which was delivered to him by top Chinese diplomat Dai Bingguo on January 11 in New Delhi.
"China-India relations have maintained stable development in the past few years, which has brought about substantial benefits to the two countries and the two peoples," state-run Xinhua news agency quoted Xi as saying.
The world has enough space for China and India to achieve common development, and the world also needs common development, he said.
Dai, the chief negotiator of the India-China border talks was in New Delhi last week to attend the Brazil, Russia, India, China, South Africa (BRICS) top security officials meeting.
Xi's letter was stated to be in response to a letter from Singh after his election as the General Secretary of the Communist Party of China (CPC) succeeding Hu Jintao.
Singh's letter conveying his greetings to the new Chinese leadership as well as assurance to carry forward the relations was handed over by National Security Advisor Shivshankar Menon last month when he visited Beijing.
Dai would be retiring from the post of State Councillor and top diplomat of the China after a decade during which he held 15 rounds of talks with Menon and several of his predecessors.
In his meeting with Singh, Dai said in the past 10 years, China and India have seen great development in their bilateral relations.
The two nations have efficiently controlled their disputes and differences and have pushed forward development of bilateral ties, while gradually finding a pragmatic way of maintaining friendly relationship of co-existence between them.
He said that in the next five to 10 years, China and India will see a strategically important period of opportunities to develop their relations.
Dai expressed his hope that the two countries will highly cherish, maintain and develop the momentum of good ties while expressing confidence that China-India relations will see greater and better development with the care and guidance of the leaders of the two countries.