Diplomatic tensions and the "aggressive policy" of the U.S. toward Moscow are of more concern than economic sanctions, the president and chairman of one of Russia's largest lenders said Tuesday.

"What concerns me more than any economic sanctions, that for the first time since the Cuban (missile) crisis — people, at least in Russia and probably in America also, have started to feel that there is more danger of World War III," Andrei Kostin, the president and chairman of Russia's VTB Bank told CNBC's Geoff Cutmore in Moscow.

"There is a recent public opinion poll (in) Russia (that) showed that 55 percent of Russians now believe or think that World War III is possible because of the aggressive policy of the United States," he added.

"It's very, very serious to reflect on what's happening in national affairs. The world is becoming a much more dangerous place to live," he said. "And that's a great concern."

Kostin's comments come amid a cold front — the coldest in a while — between Russia and the West. Among the sources of tension are Russia's support for the authoritarian regime in Syria, a suspected Moscow-directed nerve agent attack on U.K. soil, and alleged meddling in elections in the U.S. in 2016, alongside accusations of state-sponsored cyber warfare.

Russia is already experiencing ongoing Western-led economic sanctions for its annexation of Crimea in 2014 and its perceived support for a pro-Russian uprising in eastern Ukraine that same year.