Dempsey said ISIS fighters have been putting pressure on the outskirts of the city “and in fact, into the city itself.” That leads him to believe “it may be about to fall.”
For the past two weeks ISIS fighters have pressed to capture the Kurdish city, forcing thousands of residents to flee into Turkey.
If ISIS should take the city from Kurdish defenders it would be in control of most of the northern Syrian border area.
“They've got forces on their side of the border that will prevent ISIL from making any incursions into Turkey,” said Dempsey, using an alternate name for ISIS. “But, of course, ISIL is smart enough not to do that.”
In recent days the Turkish army has positioned as many as 20 tanks on its side of the border across from Kobani.
The U.S. has conducted more than a dozen airstrikes around Kobani in an attempt to push back ISIS fighters on the city’s outskirts, Pentagon officials said.
But those airstrikes have only a limited effect as Dempsey noted that they occur “when we can." ISIS fighters are “a learning enemy and they know how to maneuver and how to use populations and concealment,” said Dempsey. “So when we get a target, we'll take it.”
But finding ISIS fighters to target from the sky has become more difficult.
“They're becoming more savvy with the use of electronic devices,” said Dempsey. “They don't fly flags and move around in large convoys the way they did. ... They don't establish headquarters that are visible or indentifiable.”
Dempsey said most of the city’s residents have fled across the border into Turkey but he has “no doubt” that if the city falls ISIS will conduct “horrific atrocities if they have the opportunity to do so.”
See more of the interview with Gen. Dempsey on this Sunday’s broadcast of “This Week with George Stephanopoulos.”