Nepal raised objection to India's newly-inaugurated road linking Lipulekh Pass with Dharchula in Uttarakhand.
Senior commanders of the two armies held intense negotiations for nearly 11 hours on Sunday at a designated meeting point in Moldo on the Chinese side of the Line of Actual Control.
In the review meeting, Singh told the top military brass to continue to deal with the situation in eastern Ladakh and other areas with "firmness".
There was no comment from the Indian side on the statement made by the Chinese defence ministry spokesperson Colonel Wu Qian, and carried by China's official media.
Lauding the bravery displayed by the soldiers, the prime minister said: "The bravery that you and your compatriots showed, a message has gone to the world about India's strength."
On Tuesday, Pompeo and Esper will hold the 2+2 talks with External Affairs Minister S Jaishankar and Defence Minister Rajnath Singh, covering the entire expanse of defence and security ties as well as key regional and global issues.
Army Spokesperson Colonel Aman Anand said troops from China's People's Liberation Army (PLA) 'violated' the consensus arrived at during military and diplomatic engagements on the ongoing standoff in eastern Ladakh, and carried out provocative military movements to change the status quo.
The joint statement said Jaishankar and Wang agreed that both sides should take guidance from the series of consensus reached between leaders of the two countries on developing India-China relations, including not allowing differences to become disputes.