"I do see areas where we can cooperate, but they are getting narrower and narrower over time," Carter said in an interview with Bloomberg on Tuesday.

"That's the trajectory Russia has been on" because "that common ground to work on has been reduced over the last 10 years progressively. That's just the fact of where we find ourselves now," he said.

Read alsoTrump’s advisor on Moscow visit says fate of Russia sanctions unclearDays before the inauguration of President-elect Donald Trump, who has vowed to seek improved relations with Putin, Carter said that option is "still possible" where U.S. and Russian interests overlap, such as blocking North Korea's nuclear weapons program and preventing Iran from having one.

Yet such cooperation has "decidedly not been the case" in fighting Islamic State terrorists in Syria, he said. While Trump has talked of such a joint effort, the Pentagon has found its attempts to support a "moderate" opposition in Syria undercut by Putin's military support for the regime of President Bashar al-Assad.

Carter's frame of reference for potential cooperation dates to the early 1990s when, as a Pentagon policy official, he helped Russia emerge from a nuclear weapons-laden Soviet Union after its collapse, "making sure there was not nuclear chaos as a consequence of the disintegration," he said.

Carter said Russia also "found a way that it could be in both our interests and NATO's interests to work together in the Balkans," where ethnic conflict raged in the 1990s after the disintegration of Yugoslavia. "So I've done that and it is possible" to work with Russia, he said.

"But if the government of Russia defines its interests not only as different from the United States, which we expect, but as deliberately in opposition to the United States, it's very difficult to build a bridge to that motivation – and that's the challenge going forward," said Carter.

As UNIAN reported earlier, Russian President Vladimir Putin said January 17: "It seems that they trained for this in Kyiv and now are ready to organize a 'Maidan' in Washington not to let Trump assume office."