Premier Li was speaking during a joint address with his Indian counterpart, PM Manmohan Singh, in the capital, Delhi.
Mr Singh said special representatives from the two countries would meet soon to discuss ways to end the row.
The meeting comes after a recent flare-up in border tensions.
Premier Li arrived in Delhi on Sunday in the first stop of his maiden foreign trip since taking office.
The two neighbours are the world's two most populous countries.
During Monday's talks, the two sides discussed trade ties and other bilateral issues and signed eight agreements.
"We don't deny there are problems between the two sides," Premier Li said. "We need to improve border related mechanisms and make them more efficient," he added.
"Both Mr Singh and I believe there are far more interests than differences between our two sides. We need to confront issues with a broad mind, and tackle them in a mature way," he said.
PM Singh said India and China had "agreed that our special representatives will meet soon to continue discussions seeking an early agreement on a framework for a fair, reasonable and mutually acceptable boundary settlement".
"Peace and tranquillity on our border has to be preserved," he said.
A decades-long border dispute flared up last month after India accused Chinese troops of crossing the countries' de facto frontier.
The dispute over the territory in the Ladakh region has dogged the two countries since the 1950s.
At an informal meeting on Sunday night, Mr Singh told Mr Li that a recent military standoff on the Himalaya border could affect relations between the two countries.
Both sides, however, were keen to ensure that the border spat did not derail a general warming in relations between the neighbours and the two leader talked of "more shared interests than differences".
China is already one of India's top trading partners and both countries have already agreed a new $100bn (£65bn) bilateral trade target for 2015.
Premier Li said he had agreed to address India's concerns about the size of the trade deficit with China.
On his arrival in Delhi, Premier Li said said his decision to choose India for his first foreign visit since taking office "indicates the great importance Beijing attaches to its relations" with Delhi.
During his three-day visit in India, he is also expected to meet Indian President Pranab Mukherjee, Congress party chief Sonia Gandhi and leader of the opposition in the Lok Sabha [the lower house of Indian parliament] Sushma Swaraj.
He is also scheduled to address university students in Delhi and business leaders in Mumbai, India's financial capital, before travelling on to Pakistan, Switzerland and Germany.-British Broadcasting Corporation
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