Russian President Vladimir Putin discussed the incident on the Azerbaijan-Armenia border with his Azerbaijani counterpart Ilham Aliyev in a telephone talk Wednesday.
The two leaders stressed that they are in favor of resolving this issue through political and diplomatic means, the Kremlin said in a statement.
"The Russian side will continue to mediate and provide advisory assistance aimed at reaching an agreement between Azerbaijan and Armenia on launching the process of delimitation and demarcation of the state border," it said.
Armenia voiced protest after the Azerbaijani army settled certain sites in Lachin and Kalbajar provinces which were liberated from Armenian occupation last year.
Aliyev said Armenian Prime Minister Nikol Pashinyan "overreacted."
Moscow said it occurred because of the absence of any border for a period of time and suggested that it would help regarding borders delimitation.
Relations between the two former Soviet republics of Armenia and Azerbaijan have been tense since 1991 when the Armenian military occupied Nagorno-Karabakh, also known as Upper Karabakh, a territory internationally recognized as part of Azerbaijan, and seven adjacent regions.
Last year, the conflict escalated again and lasted six weeks, ending up with a Russian-brokered truce.
During that time, Azerbaijan liberated several strategic cities and nearly 300 of its settlements and villages from Armenian occupation. The two countries signed a Russian-brokered agreement on Nov. 10 to end fighting and work toward a comprehensive resolution.
A joint Turkish-Russian center was established to monitor the truce. Russian peacekeeping troops have also been deployed in the region.