The Chinese soldier was arrested by Indian troops after crossing the LAC, the de facto border between the two countries. The reason why the soldier crossed the LAC is under investigation, the statement said.
The strategically located lake, approximately 4,267 meters above sea level, spans an area stretching from Indian territory from Ladakh to Chinese-controlled Tibet, in the Greater Kashmir region where India, the China and Pakistan all claim territory.
The LAC, which marks the de facto border, crosses the lake.
In September, China and India agreed to stop sending more troops to the disputed Himalayan border, following escalating tensions between the two nuclear powers.
In a joint statement, the two sides agreed to strengthen communication on the ground to avoid misunderstandings or actions “that could complicate the situation.”
They also agreed not to take any unilateral action that would change the situation on the ground, the statement said.
India and China share a 2,100-mile (3,379-kilometer) border in the Himalayas, but both sides claim territory on either side of it.
The LAC was created in the wake of the 1962 Sino-Indian War and appears on the maps, but India and China do not agree on its exact location and regularly accuse the other of overtaking or seeking it. to expand their territory.
In 1996, the two countries signed an agreement which states that neither side should open fire within 2 kilometers (1.24 miles) of the LAC to “prevent dangerous military activities”.
CNN’s James Griffiths and Helen Regan contributed to this report.