"Our partners are aware of Russian principal position that Ukraine's NATO membership will undermine European security," Xinhua quoted Meshkov as saying.
Ukrainian President Petro Poroshenko said earlier in the day that Kiev should consider abandoning the country's nonalignment status in order to allow Ukraine to join military alliances.
With regard to Poroshenko's statement, Meshkov reiterated that such a step would have "tremendous" geopolitical consequences.
"Those who today are trying to drag Kiev into NATO should take on enormous geopolitical responsibility," reiterated Meshkov.
He said although any country has a right to make its choice, it is important for countries like Russia to consider the interests of European and global security first and foremost.
Poroshenko said on Monday that a referendum will be held to decide whether or not Ukraine should join NATO.
According to him, Ukrainian authorities have been working out certain criteria, which the country should meet within the coming years to obtain NATO membership.
Nevertheless, the Ukrainian president insisted that the attempt to join the alliance now "will bring more harm than advantages."
Ukraine and NATO established their partnership in 1991, shortly after Kiev gained its independence from the former Soviet Union. Ukraine closely cooperates with the alliance and actively participates in NATO's Partnership for Peace Programme.
In March 2010, the Ukrainian parliament approved a law which bars the country's membership in any military blocs but allows cooperation.