India’s External Affair Ministry spokesperson, Anurag Srivastava revealed both sides had decided to handle the situation responsibly.
Mr Srivastava speaking in a statement: “making exaggerated and untenable claims is contrary to this understanding.”
This comes after Monday’s altercation between the two sides where 20 Indian troops were killed, the biggest clash in 45 years.
China is yet to confirm if it suffered any casualties.
New Delhi Television reported that 76 Indian soldiers sustained injuries following the battle.
However, all soldiers remain in stable condition.
The Indian Army did not comment on the soldier’s injuries, whilst the Defence Ministry spokesperson Colonel Aman Anand did not immediately reply to a text message asking for his view.
Indian officials have also dismissed suggestions that any of its troops were held in Chinese custody.
Both India and China have accused each other of starting the battle which took place in the Ladakh region along the Himalayan frontier.
Soldiers tackled opposite forces with clubs, rocks and their fists.
It is believed that no shots were fired.
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He added: “After the incident, China and India communicated and coordinated through military and diplomatic channels.
“The two sides agreed to deal fairly with the serious events caused by the conflict in the Galway Valley, and … cool down the situation as soon as possible.”
The increased tensions come at a time when the coronavirus has already increased anti-Chinese sentiments in India.
India has recorded more than 366,000 virus cases, with 12,200 deaths.
Indian opposition Congress party leader Rahul Gandhi called for a response from the army.
He said: “Why were our soldiers sent unarmed to martyrdom?”
The clash followed rising tensions that began in early May after Indian officials claimed Chinese soldiers crossed the border in three places.
Officials said that soldiers had erected tents, guard posts and ignored calls to leave.
The clash led to shouting matches, stone-throwing and fistfights.