Li, who made India the first stop on his first foreign tour since becoming the China's No. 2 leader, arrived in New Delhi Sunday on a three-day trip.
The visit comes after last month's tense situation resulting from a border incident in the Ladakh region of the Himalayas in which India charged China set up tents in Indian territory, an allegation China denied. India also moved troops to the area.
The standoff ended this month after both sides withdrew but the incident marked the prevailing tensions, which go back to 1962 when the countries went to war over disputed borders.
The unsettled border has remained a thorny issue since then although overall bilateral relations, with much emphasis on trade, have improved.
Besides the border issue, China's closeness to Pakistan and India providing asylum to exiled Tibetan spiritual leader the Dalai Lama also remain irritants.
The once-in-a decade change of leadership in China that saw the rise to the top of Li and President Xi Jinping, both seen as reformers and moderates, however, have raised hopes for a resolution of the border disputes.
Besides India, Li also is to visit Pakistan, which is also going through a leadership change, Germany and Switzerland.
In one of its articles ahead of Li's trip, the official Xinhua News Agency said the choice of India as Li's first stop "sent out a clear signal that Beijing's new leadership prioritizes enhancing ties with New Delhi despite border spats and other disputes."
"With China and India being the world's two largest developing countries and most populous nations -- accounting for about 40 percent of the global population, a sour and bitter relationship would serve the interests of neither side," it said.
The article said in their recent talks with Indian Prime Minister Manmohan Singh, both Xi and Li reaffirmed China's commitment to "fostering stronger bilateral ties while effectively managing border problems and other thorny issues."
In another article, Xinhua said Li's India visit comes only weeks after Xi had a much-publicized meeting with the Indian prime minister in South African on the sidelines of the BRICS summit. BRICS is a grouping of five leading emerging economies of Brazil, Russia, India, China and South Africa.
"Such a short time interval in top-level contacts between the two Asian giants gives the impression the Chinese dragon and the Indian elephant are about to tango toward better ties and closer cooperation. And such a prospect would also bring extra glamour to multilateral frameworks such as BRICS, in which China and India are major players,"
the article said.
It went on to say visionary leaders in both countries have realized the "world has sufficient room for the development of China and India and the two neighbors share vast common interests, despite their lingering border issues and the much-hyped China-India rivalry for regional primacy."
India and China were expected to sign a series of cooperative agreements during Li's visit.
India, however, remains concerned about the Ladakh incident.
Singh, in his Sunday talks with Li, said "peace and tranquility" on the border is the "foundation" of the bilateral ties and any disruption will impact the relationship, the Hindustan Times reported.
Singh also urged China to share more information about its activities concerning trans-border rivers. This issue has come up because of concerns China plans to build three dams on the Brahmaputra River, a vital source of water for India.
The countries have promised to increase bilateral trade to $100 billion by 2015 but Singh expressed India's concern about the growing trade imbalance and called for greater access to Chinese markets for Indian products. Critics say India's exports to China are mostly raw materials such as iron ore, while Chinese exports are finished products.
On the Dalai Lama issue, Singh informed Li that while the spiritual leader is an honored guest, India wouldn't allow its territory to be used for anti-China activities.
Li said peace and regional stability cannot be a reality without strategic mutual trust between China and India, the Press Trust of India news agency reported. "And likewise the development of prosperity of the world cannot be a reality without the cooperation and simultaneous development of China and India."
The Times of India said Li's Indian hosts found him to be surprisingly engaging and easy to like.
Li is also to visit Mumbai, India's financial capital, to meet with Indian business leaders.
Toddler uninjured after being knocked over by Obama family dog
Texas principal bans speaking Spanish, stirs controversy