Elder statesman Henry Kissinger on Sunday said the Russians are eager to help the U.S. resolve the Syrian chemical weapons crisis to make sure the radicals involved in that civil war do not become a problem for President Vladimir Putin.

"I would think [Putin's] biggest security problem is radical Islam," Kissinger told CBS's "Face the Nation."

"He does not want the United States to look totally irrelevant in the Middle East, because otherwise he would be stuck with having to deal with radical Islam," Kissinger said.

Putin has already stepped up Russian security agency involvement in the North Caucasus region where he says terrorists and criminals are trying to gain a foothold in advance of the 2014 Winter Olympics in Sochi.

"There's also a necessity for the selfish interests of both sides for cooperation, especially if one looks at the long term situation of Russian," Kissinger said.

In that sense, Russia can be trusted to carry out the Syrian agreement negotiated by Secretary of State John Kerry, but that does not mean Putin "has suddenly been converted to our point of view," Kissinger said.

Speaking about the United Nation's General Assembly next week, Kissinger dismissed suggestions from the White House that President Barack Obama might meet with Iran's new president, Hassan Rouhani.

"Iran has been building with great energy a nuclear program, and I would be more at ease if the meeting of the president occurred at the end of some diplomatic achievement," Kissinger said. "But I can see the temptation."