In the greeting posted in his account in Weibo, China's popular microblog, PM Modi said "our relations date back to centuries, encompassing spiritualism, learning, art, trade and respect for each other's civilisation and shared prosperity".
"As I have said earlier, both our countries reflect, in many ways, similar aspirations, challenges and opportunities, and can be inspired by each other's successes."
"At a time when the world looks towards Asia, the progress and prosperity of China and India, and our close cooperation, have the potential to shape a peaceful and stable future for Asia," he said.
This is a vision I share with President Xi and Premier Li Kiqiang, he said.
"In recent times, we have deepened our engagement across the full spectrum of our ties, and laid emphasis on deepening mutual trust and confidence, and expansion of people-to-people ties.
"And we will continue our endeavours in this direction," he said.
PM Modi, who opened his account on Weibo ahead of his China visit last year, has thousands of followers in the country. China celebrated its 67th national day today with special ceremonies marking the occasion.
Meeting the foreign experts working in China who were conferred Friendship Awards, Li said China is ready to welcome more talent from abroad as the country becomes more open and inclusive.
Earlier Vice-Premier Ma Kai conferred medals on the 50 foreign experts and praised their contribution to the country's development at an awards ceremony in Beijing.
Mr Li observed that the foreign experts in China include both young and old, and the combination of their brainpower and great experience could "help yield a greater boost to China's modernisation process and world peace and development".
He said China is offering greater openness, inclusiveness and convenience for outstanding foreign talent, and the country will speed up facilitation of their application for a permanent residence permit.
Mr Li and others also greeted foreign ambassadors and envoys assuming their new offices in China.
Mr Li said China is committed to peace and development, and will join hands with countries to "achieve robust, sustainable, balanced and inclusive growth".