He greeted the people of China on their National Day.
In his message, Modi said: "There have been strong linkages between our nations for years. Together we can make this world a much better place. The growth of India and China offers a great opportunity to realise our dream of an Asian century."
He recalled Chinese President Xi Jinping's visit to India in September 2014 and his visit to China in May 2015 and said the meeting "covered significant ground in advancing our partnership".
"I warmly recall my talks with President Xi and Premier Li," he added.
"I am confident that our ties will become stronger in the years to come. May our two nations continue working together for the common development and prosperity of humanity," Modi said.
The Chinese government passed a resolution on December 2, 1949, and declared October 1 as the National Day.