Li, during his official three-day visit to India, said the two countries had "established principles for settling the question" of where the border should lie, The Hindustan Times reported.
The goal is to avoid disagreements that in the past have threatened to spill over into armed clashes.
"Both sides believe we need to improve the border mechanisms that have been put into place and make them more efficient and appropriately resolve our differences," Li said on his first foreign trip since taking office in March.
"On the basis of deeper trust, our two countries can further deepen our mutual understanding and construct a new type of relationship between major countries, promote healthy and sound development of China and India.
"World peace ... can't be a reality without strategic trust between India and China," he said. "That will be a true blessing for Asia and the world."
Singh said during the joint press conference that special representatives from both countries will meet soon to continue discussions "seeking an early agreement on a framework for a fair, reasonable and mutually acceptable boundary settlement."
Singh said "peace and tranquility on our border has to be preserved."
Neither leader mentioned the latest dispute in April when Chinese patrols in the Ladakh region moved about 12 miles into what India claims as its side of the Line of Actual Control, the de facto border in the rugged Himalayan region.
The Chinese set up camp around 500 feet from an Indian patrol camp and continued a face-off.
There were no reports of hostilities and the move was suspected only to raise the wider issue of demarcation, which has suffered from "difference of perception between India and China," an Indian official reportedly said during the dispute in April.
However, the faceoff was enough for New Delhi to send India's foreign minister to Beijing for discussions, likely with a view to smoothing the impending visit to India of the Chinese premier.
The Himalayan region has been the focus of several armed conflicts since 1947 when the British quit the subcontinent, creating India and Pakistan out of the colonial territories.
China and India fought a brief indecisive war over the region's ill-defined border in 1962 and the two countries since have carefully patrolled the region.
But border issues have been more intense with Pakistan to the west, including military clashes in 1947, 1965 and 1999.
India and Pakistan agreed on a Kashmir cease-fire line in 2003 although Pakistan claims all of India's Jammu and Kashmir state, which is around 60 percent Muslim -- India's only Muslim majority state.
Li arrived in New Delhi on Sunday and will be meeting Foreign Minister Salaman Khurshid, ruling Congress party leader Sonia Gandhi and senior figures from the main opposition Bharatiya Janata Party, The Hindustan Times said.
He will head off to India's financial center Mumbai today in an effort to reassure the value of doing business with China, India's second-largest trading partner.
India-China trade was around $66.5 billion last year, a drop from $74 billion in 2011.
Even so, trade remains targeted to reach $100 billion by 2015, Chinese vice commerce minister Jiang Yaoping told reporters last week.
But India also faces an increasing trade deficit with China, reaching around $29 billion last year, The Hindustan Times report said.
Li's next stop is Pakistan before visiting Switzerland and Germany.
Despite the smiles between the two leaders, tensions will remain in the wake of Li's visit, a report by the BBC said.
India insists on the return of territory in the northwest and China claims a large part of Indian territory in the northeast.
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