"If the American president isn't going to take the lead, if he's going to continue to regard this as a law enforcement matter, … we're not going to be able to lead and we're going to have another 15 months of the world believing we are sort of flaccid dupes. We're unlikely to do anything substantially important in pulling together a coalition," he said.
French fighter jets launched their biggest raids in Syria to date on Sunday targeting the Islamic State's stronghold in the city of Raqqa. The operation was carried out in coordination with U.S. forces.
Jack Jacobs, a retired U.S. Army colonel, said in another "Squawk Box" interview he, too, does not expect the U.S. to send military forces to fight ISIS in the near future.
"I think [we'll see] more of the same [of] what we've seen before: targeting various places where we've had some intelligence, but these are all tactical strikes. There is no strategic plan or a strategic objective," he said.
These attacks could also give rise to right-wing parties in Europe and could move the continent closer to Russian President Vladimir Putin, Robert Hormats said Monday.
"The problem with these right-wing parties, in addition to their very tough rhetoric, ... most of them are anti-American, most of them are anti-NATO, most of them are complicit with Putin," Kissinger Associates' vice chairman told CNBC.
— Reuters contributed to this report.