The incident follows rising tensions, and is the first deadly clash in the border area in at least 45 years.
The Indian army initially said three of its soldiers had been killed, adding that both sides suffered casualties.
But later on Tuesday, officials a number of critically injured soldiers had died of their wounds.
India's external affairs ministry accused China of breaking an agreement struck the previous week to respect the Line of Actual Control (LAC) in the Galwan Valley.
Early on Tuesday the Indian army said three of its soldiers, including an officer, had died in a clash in the area.
Later in the day, it released a statement saying the two sides had disengaged.
It added that "17 Indian troops who were critically injured in the line of duty" and died from their injuries, taking the "total that were killed in action to 20".
China did not confirm any casualties, but accused India in turn of crossing the border onto the Chinese side.
Chinese foreign ministry spokesman Zhao Lijian said India had crossed the border twice on Monday, "provoking and attacking Chinese personnel, resulting in serious physical confrontation between border forces on the two sides", AFP news agency reported.
Local media outlets reported that the Indian soldiers had been "beaten to death" but there was no confirmation from the military. China's Global Times newspaper reported that "solemn representations" had been made with India.