Mr Shoigu told President Vladimir Putin in televised remarks that Russia on Wednesday morning carried out 26 missile strikes from four warships of its Caspian Sea flotilla.
Mr Shoigu insisted the operation destroyed all the targets and did not launch any strikes upon civilian areas.
US defence secretary Ash Carter said the US-led coalition has not agreed to co-operate with Russia in the fight against IS and no collaboration is possible as long as Moscow continues to strike other targets.
He said the US will conduct basic, technical talks with Russia about efforts to ensure that flights over Syria are conducted safely, and: "That's it."
The US, Mr Carter said, is not prepared to co-operate with a strategy of Russia's that is "tragically flawed".
"They continue to hit targets that are not Isil," Mr Carter said, using an acronym for IS. "We believe that is a fundamental mistake."
Mr Carter said he is concerned about the Syrian ground offensive that began on Wednesday backed by Russian airpower.
Russia, which backs Syrian president Bashar Assad, has hit Western-backed rebels fighting Assad. The US maintains that the only route to peace in Syria is to remove Assad from power.
Russia on Tuesday informed the US that Moscow is willing to continue talks to ensure that the two countries' aircraft do not interfere with each other, US officials said. But a Russian defence official said the talks should be much broader than what the Pentagon is seeking.
Britain's UN ambassador said Russia's military actions in Syria are strengthening IS by strengthening Syrian president Bashar Assad and forcing much of Syria's Sunni population "into the arms" of the extremist group.
Matthew Rycroft told a group of reporters that "Russia's military action is a significant escalation of this crisis".
He said that while the Russians say they are attacking IS extremists, anyone looking at a map of their strikes can see that most "are against what we consider the moderate opposition to Assad, the very people that we need to be part of the future of Syria".
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