Russia has demanded that the US and the European Union guarantee the NATO military alliance will never let Ukraine join the bloc.
They have refused to do so but sent their own proposals to Russia.
Shoigu urged the US and its allies to stop supplying arms to Ukraine and said Russia was not the one to blame for the rising tensions in Europe.
He also said he wanted to know why the UK was sending special forces to Ukraine.
Russia has amassed more than 100,000 troops near its border with Ukraine but denies that it plans to invade its neighbour.
US Secretary of State Antony Blinken said on Friday that a Russian invasion could come at any time, perhaps before the end of this month's Winter Olympics.
Russia meanwhile dismissed answers sent this week by the EU and NATO to its security demands as an insult.
Commercial satellite images published by a private US company showed new Russian military deployments at several locations near Ukraine.
In his starkest warning yet to US citizens in Ukraine to get out now, President Joe Biden said he would not send troops to rescue US citizens in the event of a Russian assault.
"Things could go crazy quickly," Biden told NBC News.
Blinken, visiting Australia, told a news conference: "We're in a window when an invasion could begin at any time, and to be clear, that includes during the Olympics."
The Beijing games end on February 20.
"Simply put, we continue to see very troubling signs of Russian escalation, including new forces arriving at the Ukrainian border," Blinken said.
Russia's Chief of General Staff Valery Gerasimov and US Joint Chiefs Chairman General Mark Milley held phone talks on Friday, Interfax news agency reported, citing a Russian defence ministry statement.
They discussed international security, the agency added without giving further details.
Russia this week launched joint military exercises in neighbouring Belarus and naval drills in the Black Sea.
Russia denies plans to invade Ukraine but says it could take unspecified "military-technical" action unless a series of demands are met, including promises from NATO never to admit Ukraine and to withdraw forces from eastern Europe.
Four-way talks in Berlin between Russia, Ukraine, Germany and France, part of a longstanding peace process in a conflict between Ukraine and Russian-backed separatists, yielded no progress on Thursday.
France and Ukraine said the Russian delegation had demanded Ukraine negotiate directly with the separatists, a "red line" Ukraine has rejected since the conflict began in 2014.
"If Ukraine agrees to this, then the status of Russia will change from being a party to the conflict to the status of being a mediator in the conflict. That is why we do not go for it," Ukraine's Foreign Minister Dmytro Kuleba said.
