The statement by Russia's foreign ministry contradicted a declaration by US Secretary of State John Kerry made after a meeting in Paris on Tuesday with his Russian counterpart Sergei Lavrov.
Moscow "will not join any 'coalition' set up without the backing of the UN Security Council and that violates international law," the ministry said.
It pointed out that a bilateral commission involving Washington and Moscow that aimed to help tackle terrorism had been scrapped by the US.
The slapdown to Kerry appeared to underline yet again the fraught state of US-Russian relations, brought low by the crisis in Ukraine where pro-Russian rebels are fighting a pro-West government.
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Kerry had said on Tuesday that he and Lavrov reached an agreement "to intensify intelligence cooperation with respect to ISIL (Islamic State) and other counter-terrorism challenges".
He said Lavrov had "acknowledged their preparedness to help with respect to arms, weapons, they are doing that now, they already have provided some, and also potentially with the training and advising aspects".
The two sides are also at loggerheads over the civil war in Syria, where Moscow has been a staunch ally of President Bashar al-Assad.
Washington is currently spearheading a coalition of Western and Arab nations conducting an air campaign against the Islamic State jihadists.