Moscow's appeal came after Turkish President Recep Tayyip Erdogan on Monday demanded Armenia put an end to its "occupation" of Nagorny Karabakh and called for Armenia to leave the territory, which is internationally recognised as part of Azerbaijan.
"We call on all sides, especially partner countries such as Turkey to do all they can for a ceasefire and get back to a peaceful settlement of this conflict using political and diplomatic means," Kremlin spokesman Dmitry Peskov told journalists.
"Any statements about some kind of support and military activity undoubtedly add fuel to the flames. We are categorically against this."
Armenia has accused Turkey of sending mercenaries to back Azerbaijan, its close ally.
Turkey and Armenia have extremely strained ties.
Read also: Armenia and Azerbaijan: a decades-long bloody rivalry
Peskov said that Russia was in "constant contact" with all three countries.
Russia is part of a military alliance of former Soviet states that includes Armenia and has a military base there.
However, Russia supplies weapons to both Yerevan and Baku.
France, Russia and the United States have mediated peace efforts as the "Minsk Group", but the last big push for a peace deal collapsed in 2010.
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