Writing in The Hindu newspaper, Li warned that there would be no Asian century if India and China failed to live in harmony and achieve common development.
"There is no denying that China and India still have between them some difficult issues left over from history," he said in the article titled "A handshake across the Himalayas".
"But the rich historical experience and the broad vision... serve as the basis for China and India to take a long-term view and live in amity with each other."
He added: "China and India, two big Asian countries living next door to each other, are destined to be together."
In his article, Li paid glowing tributes to Indian history and culture as well as economic strengths and described India as a nation "at once old and young".
He said both countries "agree that the common interests between China and India far outweigh their differences and that the two countries should enhance mutual trust rather than increasing mutual suspicion..."
"As long as we face the problems squarely and talk to each other with sincerity, we will eventually find proper solutions (to our differences)."
Li underlined the point by saying that India and China "need to live with our neighbours in harmony and make friends in the world".
The Chinese premier, who arrived here Sunday on a three-day visit, his first since taking office in March, said China had a long way to go to achieve modernisation despite its present strength.
"Even if China becomes strong one day, it will never embark on the doomed path of seeking hegemony," he said.
He said Asia's future depended on China and India.
"If China and India live in harmony and prosper together, and if our two markets converge, it will be a true blessing for Asia and the world at large."