Kremlin spokesman Dmitry Peskov branded the allegations "absurd" and "irresponsible".
"Russia has not, does not and will not interfere in the internal affairs of another state, particularly Montenegro with which we enjoy very good relations," he told journalists.
Russian Foreign Minister Sergei Lavrov also denounced what he said were "baseless allegations against us and our country".
Montenegrin special prosecutor Milivoje Katnic on Sunday accused the Russian state of involvement in the alleged plot to seize parliament and assassinate former premier Milo Djukanovic during the October election.
"So far we have had evidence that Russian nationalist structures were behind (the plot), but now also that Russian state bodies were involved at a certain level," Katnic told local media.
"The organs of the Russian state must investigate which bodies are involved and open a criminal trial over these acts."
Montenegrin prosecutors suspect 25 people, mostly Serbs, of links to the alleged coup, and have launched a manhunt for two Russians.
One of the suspects is Eduard Sismakov, an aide to Russia's military attache in Poland who is believed to be the architect of the plot aimed at preventing Montenegro from joining NATO, Katnic said.
The suspects also include two leading pro-Russian lawmakers from the opposition Democratic Front (DF), which is strongly opposed to Montenegro's bid to join NATO but denies any involvement in the plot, claiming the affair was fabricated by the government.
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