Russian President Vladimir Putin also took part in the meeting between Azerbaijani President Ilham Aliyev and Armenian Prime Minister Nikol Pashinyan, which was held in the Black Sea port of Sochi.
The worst fighting between the two countries since a 2020 war erupted last month, killing more than 200 people. The clashes took place despite agreements in both 2020 and 2021 to find a peaceful solution.
“We agreed to refrain from the use of force or threatening force, to discuss and resolve all problematic questions solely on the basis of mutual recognition of sovereignty, territorial integrity and the inviolability of borders,” RIA cited a statement as saying, Reuters reported.
The clashes are linked to decades-old hostilities over control of the Nagorno-Karabakh region.
It is internationally recognized as part of Azerbaijan, but until 2020 largely controlled by the majority ethnic Armenian population.
Earlier this month the two sides agreed a civilian European Union mission should head to the border to assess the situation.
Moscow, which has a defense pact with Armenia and a military base there, deployed thousands of peacekeepers to the region after a ceasefire in 2020.