"A complete ban should be introduced on any drills related to honing skills of using nuclear weapons by troops of non-nuclear states", Ryabkov said.
The diplomat added that Washington had not responded to Russia's proposal to issue a joint statement on the avoidance of a nuclear war.
Ryabkov stressed that the US handing over its nuclear weapons to non-nuclear states goes against the Treaty on the Non-Proliferation of Nuclear Weapons.
"This… creates additional obstacles for nuclear disarmament. This problem can have only one solution — the return of all US nuclear weapons to the US, a ban on their use abroad and demolition of the infrastructure that allows using these weapons fast", Ryabkov said.
NATO's policy of nuclear deterrence relies partly on US nuclear arms deployed in Europe.
Speaking further, Ryabkov said that the United States had submitted its justification for deploying Terminal High Altitude Area Defence (THAAD) system to Romania, while Moscow was studying the reasons.
"Yes, we have received a certain amount of information and justifications for the temporary deployment of… THAAD systems during relevant works at the missile defence facility… We have taken this into account, we are studying these reasons", Ryabkov told a briefing.
The United States' European Command has said that THAAD would be moved to Romania in the summer during maintenance work on the Aegis Ashore located there.
On Possible Nuclear Agrement
According to the senior official, Russia will analyse all US ideas on a new nuclear agreement if and when it receives specific proposals from Washington.
"If we receive specific proposals, of course, we will analyse what the US side might offer us and contact them over the matter", the diplomat said.
CNN reported earlier in the day that the White House was holding intense internal discussions to enable US President Donald Trump to pursue his intention to negotiate a major nuclear deal with Russia and China.
On North Korea
According to the deputy foreign minister, Moscow will brief Washington on the results of the recent summit between Russian President Vladimir Putin and North Korean leader Kim Jong-un after the Russian top-level delegation returns from China.
"I think, it will happen after the president and the entire delegation return from China", Ryabkov said, answering a corresponding question.