The nine countries with nuclear weapons are being taken to the International Court of Justice and in the case of the US to an American court because Washington doesn't recognise the ICJ.
The nine are accused of failing their obligations to disarm as stipulated in the Non-Proliferation Treaty.
The Russian Foreign Ministry has expressed surprise at the allegation, saying Russia and the United States had been negotiating nuclear cuts for years.
It says as a result, Russia has reduced its strategic nuclear potential by more than 80 percent and its non-strategic nuclear weapons by three-quarters from their peak numbers.
It also says Russia is convinced that filing baseless suits does not foster favourable conditions for further steps by the international community in the area of arms control and the non-proliferation of weapons of mass destruction.
Russia has also made clear it will not approve cuts below ceilings set in the 2010 New START treaty unless the United States addresses Moscow's concerns about US missile defense and non-nuclear weapons capabilities.
