Baku dismisses Yerevan's accusations that it was laying "siege" to a lake on their border, calling such claims "provocative."
Azerbaijan and Armenia are holding talks to resolve border tensions, Russia's RIA news agency cited the Azerbaijan's Foreign Ministry as saying, a day after Armenia accused its neighbour of violating its borders.
Talks began on Friday after Armenian Prime Minister Nikol Pashinyan accused Azerbaijan's military of crossing the southern border and trying to claim territory.
Armenia's prosecutor general on Thursday also opened a criminal case into "an infringement of territorial integrity", accusations Azerbaijan dismissed.
Azerbaijan dismissed the accusations on Friday, saying it was enforcing its own border and called Pashinyan's claims provocative.
Azerbaijan said its "border troops are taking positions that belong to Azerbaijan, in the Lachin and Kalbajar districts."
Following its accusations, Pashinyan's office said he had made a formal request to a Russia-led security bloc, the Collective Security Treaty Organisation (CSTO), to hold consultations.
Tensions over lake
Armenia on Thursday accused Azerbaijan's military of crossing the southern border in an "infiltration" to "lay siege" to a lake that is shared by the two countries.
Azerbaijan rejected the claims.
Western countries including the United States and France raised concerns, with tensions still high after last year's war between the longtime rivals over Nagorno-Karabakh region.
The six-week conflict claimed some 6,000 lives and ended after Armenia vacating swathes of territory it had occupied for decades.
Turning to CSTO
Pashinyan informed Russian President Vladimir Putin of his decision to turn to the CSTO during a phone call late on Thursday, his office said.
Under the treaty, members of the bloc, which also includes Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan, consider aggression against one member as aggression against them all.
"The Russian side reaffirmed its readiness to continue exerting active mediation efforts with a view to ensuring stability in the region," it said.
The Kremlin said Putin was calling on both countries to respect peace agreements, adding that Russia would continue "active mediating efforts."
Putin's spokesman Dmitry Peskov said Pashinyan had not asked for immediate assistance.
Russia calls for strict observance of truce
Putin stressed the need for strict observance of a ceasefire agreement between Armenia and Azerbaijan during the phone call with Pashinyan, according to the Kremlin.
"Pashinyan spoke in favour of constructive dialogue and cooperation, with the aim of solving all problems that arise through peaceful, political and diplomatic means," the Kremlin said in a statement.
The Kremlin said Russia was determined to continue mediation efforts and maintain close contacts with both Yerevan and Baku.
Relations between the former Soviet republics have been tense since 1991 when the Armenian military occupied Nagorno-Karabakh, a territory recognised as part of Azerbaijan, and seven adjacent regions.
When new clashes erupted on September 27, the Armenian army launched attacks on civilians and Azerbaijani forces and violated several humanitarian ceasefire agreements.
During the 44-day conflict, Azerbaijan liberated several cities and nearly 300 settlements and villages from the Armenian occupation.
The two countries signed a Russian-brokered agreement on November 10 to end fighting and work toward a comprehensive resolution.
The truce is seen as a victory for Azerbaijan and a defeat for Armenia, whose armed forces have been withdrawing in line with the agreement.