The number two in the Chinese leadership offered New Delhi a "handshake across the Himalayas" and said the world's most populous nations could become a new engine for the global economy if they could avoid such irritants.
"Both sides believe that we need to improve the various border-related mechanisms that we have put into place and make them more efficient. We need to appropriately manage and resolve our differences," Li said at a joint news conference with Prime Minister Manmohan Singh, where both men appeared relaxed.
China and India disagree about large areas on their 4,000-km-long border and fought a brief but bloody war 50 years ago.
While there has not been a shooting incident in decades, the long-running dispute gets in the way of improving economic relations between neighbours, who account for 40 percent of the world's population and whose fast growing markets stand in contrast to the stagnant economies of the West.
Bilateral trade reached $66 billion last year but both sides believe the potential is much greater. In a joint statement that seemed to address Indian gripes about its $29 billion deficit with China, they agreed to address the imbalance, with specific reference to pharmaceuticals, IT services and agriculture.
Essar Group conglomerate is set to sign a $1 billion loan deal with China's China Development Bank and China's largest oil and gas producer PetroChina during the trip, sources said. They said the loan would be backed by the supply of refined products to PetroChina.
In an impromptu speech after an official welcome ceremony at the presidential palace earlier on Monday, Li said he wanted to build trust and cooperation on his trip.
"World peace and regional stability cannot be a reality without strategic mutual trust between India and China. And likewise, the development and prosperity of the world cannot be a reality without the cooperation and simultaneous development of China and India," he said.
Li said he chose New Delhi as his first destination on the four-nation tour to show how important India is for China and also because he had fond memories of visiting as a Communist youth leader 27 years ago.
While most observers think it will take years to resolve the border dispute, recent statements from Beijing suggest China's new leadership would like to speed things up, perhaps to shift its attention to disputes elsewhere in Asia, including the South China Sea.
Singh said negotiators will meet soon to seek an early agreement on a framework to settle the border, a goal that has so far eluded representatives in 15 rounds of high level negotiations since the 1980s.
The three week stand-off on the border that ended on May 3 was the latest reminder that sensitivity runs high. It distracted diplomats' attention from talks on investment and trade ahead of Li's trip and soured public opinion toward China in India.
The disagreement over who owns barren patches of the Ladakh plateau and Arunachal Pradesh means there is almost no road or rail connectivity between the giants.
At a meeting with Singh in Durban this year, Chinese President Xi Jinping said the two countries should seek a solution "as soon as possible" - a departure from previous language. His urgency was echoed in Delhi last week by foreign ministry spokesman Qin Gang, who said the two sides needed to "redouble efforts" to reach a solution at an "early date."
That will not be easy, not least because it is politically difficult for an Indian politician to concede territory to China. Protests by nationalist groups in Delhi and Jammu and Kashmir on Monday against Li's visit highlighted anti-China feeling among some Indians.
Prior to Monday's meetings, a senior official at the foreign ministry said India was sceptical of recent overtures and will wait to see if China will bring anything new to the table.
Among the measures being looked at to reduce the risk of border confrontations is allowing higher level meetings between regional military commanders, another Indian official said.
Also raised in meetings between the leaders was the issue of the Dalai Lama, who China considers a separatist and who lives in exile in India.
India repeated its position that the Dalai Lama is a spiritual and religious leader, a senior government official said. On Monday, a protester dodged tight security to unfurl a banner saying "Tibet will be free" in front of the hotel where Li is staying in Delhi.
After India, Li is due to visit Pakistan, Switzerland and Germany and is likely to carry a message that China wants more open foreign relations and should not be seen as a threat.
"We stand ready to embrace the world with a more open mind and hope that the world will view China with a calm frame of mind," he wrote in a newspaper editorial published on Monday.