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."
Carter spoke during a press conference in Rome with Italian Defense Minister Roberta Pinotti.
The United States, Carter said, is not prepared to cooperate with a strategy of Russia's that is "tragically flawed."
"They continue to hit targets that are not ISIL," Carter said, using an acronym for the Islamic State group. "We believe that is a fundamental mistake."
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Russia yesterday informed the United States that Moscow is willing to continue talks to ensure that the two countries' aircraft don't interfere with each other, US officials said.
But a Russian defense official said the talks should be much broader than what the Pentagon is seeking.
The Pentagon wants talks aimed at making sure there are no conflicts, collisions or other problems as the US-led coalition and the Russians fly over Syria. The US side has proposed a number of safety measures, including using specific international radio frequencies for distress calls by military pilots flying in Syrian airspace.
Russian Deputy Defense Minister Anatoly Antonov said the Russians want broad discussions on international cooperation between Russia and the US-led coalition fighting the Islamic State, but "regrettably, the Americans would like to limit our cooperation to technical issues relating to interaction between our pilots."
US and Russian officials met once by video conference late last week, before Russian incursion into the airspace of Turkey over the weekend.