Increased airstrikes over the besieged Syrian city of Kobani have allowed the American-led coalition to take out large numbers of Islamic State fighters, the top American commander for the Middle East said on Friday.

Gen. Lloyd J. Austin, the head of the United States Central Command, acknowledged that the Sunni militant group might still manage to take Kobani, but indicated that even if it did, it would be a costly victory that could eventually help the United States and its allies in other parts of Syria as well as in Iraq.

“What’s going on in the Kobani area is that, in my assessment, the enemy has made a decision to make Kobani his main effort,” General Austin said during a rare appearance before reporters at the Pentagon. He said that fighters from the group, also known by the acronyms ISIS or ISIL, had poured into Kobani.

“Now, my goal is to defeat and ultimately destroy ISIL,” he said, using an acronym for the Islamic State. “And if he continues to present us with major targets, as he has done in the Kobani area, then clearly we’ll service those targets.”