The allegations were "in line with other baseless accusations against us and our country," Russian Foreign Minister Sergey Lavrov said on Monday, according to his ministry's website.
On Sunday, Montenegro's Chief Special Prosecutor Milivoje Katnic told news site Vijesti.me he had evidence that "Russian state bodies" were involved in the preparations for November's coup attempt at certain stages of the planning.
The plotters planned to prevent the country from joining NATO, Montenegrin news site Vijesti.me quoted Katnic as saying.
Russia has been anxious about the military bloc's eastward expansion for years and in 2014 annexed the Crimea Peninsula from Ukraine. Some 10,000 people have died in fighting in Ukraine since a pro-European uprising in Kiev and the ouster of a Moscow-backed president in February 2014.
According to Montenegrin officials, the perpetrators behind the attempted coup were 25 Montenegrin and Serbian nationals, including former police officers and veterans of the ongoing war in Ukraine.
Kremlin spokesman Dmitry Peskov said Katnic did not present any evidence to back claims that Russia was behind the bid.
Katnic said Sunday the accusations are backed by wiretapped phone conversations and interrogations of the suspects, but his agency, which is continuing the investigation, did not release the original recordings alleged to be in the hands of investigators.
Montenegro, a nation of some 600,000, is located more than 1,000 miles west of Russia.