"But we consider that the two countries are capable of taking necessary steps to prevent such situations in the future and to ensure that there is predictability and stability in the region and that this is a safe region for nations, first of all, China and India," Russian news agency Tass quoted Peskov as saying.
The Kremlin spokesman emphasised that China and India are Russia's close partners and allies, and "have very close and mutually beneficial relations (with Russia) built on mutual respect."
Foreign Minister Sergei Lavrov said Russia welcomed contacts between the two nations to de-escalate the situation.
The Indian Army initially said on Tuesday that an officer and two soldiers were killed. But in a late evening statement, it revised the figure to 20 saying 17 others who "were critically injured in the line of duty and exposed to sub-zero temperatures at the standoff location succumbed to their injuries."
In Beijing, Chinese Foreign Ministry officials were silent on the casualties suffered by the People's Liberation Army (PLA) troops, but Hu Xijin, the editor of the ruling Communist Party-run Global Times tabloid, tweeted to say that there are casualties on Chinese side too.
According to a report in the US News, at least 35 Chinese troops including one senior official died in the violent clash with Indian soldiers.
Chinese Foreign Minister Wang Yi spoke to External Affairs Minister S Jaishankar and the two leaders agreed to "cool down" tensions on the ground "as soon as possible" and maintain peace and tranquility in the border area in accordance with the agreement reached between the two countries, an official statement from China said.
Jaishankar told his Chinese counterpart Wang that the unprecedented incident in the Galwan Valley will have a serious impact on the bilateral relationship and asked China to take corrective steps, the Ministry of External Affairs said in New Delhi.