Relations between the two Asian powers have been fraught since a high-altitude clash that left 20 Indian soldiers and at least four Chinese troops dead in June 2020.
The neighbours have since massed tens of thousands of soldiers along the border, who remain despite 18 rounds of talks between top military officials of both countries.
Singh held talks with his Chinese opposite number General Li Shangfu on Thursday ahead of a meeting of defence ministers from the Shanghai Cooperation Organisation (SCO), which India is chairing this year.
The Indian defence minister stated New Delhi's position "categorically", a statement from his ministry said late Thursday.
"He reiterated that violation of existing agreements has eroded the entire basis of bilateral relations and disengagement at the border will logically be followed with de-escalation," it added.
India is wary of its northern neighbour's growing military assertiveness and disputes over their 3,500-kilometre (2,200-mile) shared frontier are a perennial source of tension.
China claims all of India's northeastern state of Arunachal Pradesh, considering it part of Tibet, and the two fought a border war in 1962.
Beijing and New Delhi have regularly accused each other of trying to seize territory along their unofficial divide, known as the Line of Actual Control.
The clash in 2020 along the western border dividing Tibet from the Indian state of Ladakh led to a sharp deterioration in relations, with both sides sending major reinforcements to the area.
Li said in a statement published online Friday that the situation on the border was "stable".
"We hope that both sides can work together to continuously enhance mutual trust," the statement added.
India currently holds the rotating presidency of the SCO, a forum established in 2001 which also includes Russia and Pakistan, among others, rivalling Western institutions.
Moscow's defence minister Sergei Shoigu was also in New Delhi to attend Friday's meeting, Russian news agencies reported.
India's long-standing security ties with Russia have put it in an awkward diplomatic position in the wake of Moscow's invasion of Ukraine.
Prime Minister Narendra Modi's government has walked a tightrope between India's increased security cooperation with Western countries and its reliance on Russia for defence and oil imports.
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