SURUC, Turkey — The advance of Islamic State forces on the Syrian city of Kobani has stalled as the militants have been forced to retreat on several fronts, shifting the monthlong battle increasingly in favor of the Kurdish fighters defending the city, according to commanders and Kurdish and American officials. report NYT

Dozens of airstrikes this week by the American-led military coalition killed hundreds of Islamic State fighters, allowing Kurdish units to regain territory, said Gen. Lloyd J. Austin, head of the United States Central Command, who made a rare appearance before reporters at the Pentagon on Friday.

The Kurdish fighters, General Austin added, have done “yeoman’s work in terms of standing their ground.”

The spectators who have gathered daily on the Turkish hills overlooking Kobani turned their gaze away from the quieter city on Friday to a village several miles west, where a group of Islamic State fighters had taken up positions after pulling back.

“I hear there is movement,” said Idris Bakr, a 26-year-old refugee who has been living, along with 35 members of his family, in a garage in the Turkish border town of Suruc for about a month. “God willing, it will be O.K.,” he said. “Days, we hope.”

Despite the rapid gains, General Austin warned that it was “highly possible that Kobani could still fall.” With the militants still resisting in pockets of eastern Kobani, including on a strategically important hill, and with clashes possibly looming in the surrounding villages, the Kurdish fighters were not declaring victory.

The siege of Kobani, a majority-Kurdish area hugging the Turkish border, has been freighted with symbolic, if not strategic, significance. It has become perhaps the most visible front of the war between the American-led coalition and the Islamic State, also known as ISIS or ISIL, as well as a crucible of broader tensions between Kurds and the Turkish government.

Both the United States and the militants have come to regard the city as a critical test of wills in the broader conflict in Iraq and Syria. Hundreds of Islamic State fighters had poured into the city, leading to predictions of its imminent fall as recently as last week.

“The enemy has made a decision to make Kobani his main effort,” General Austin said on Friday.

The United States responded by sharply escalating the bombing campaign in conjunction with Kurdish fighters, who supplied targeting coordinates. Though American officials denied that the situation in Kobani was a factor, the stepped-up airstrikes began as the siege became a subject of international media scrutiny: Because of an accident of geography, journalists, refugees and others were able to watch every turn in the battle from hills across the border.

“Now, my goal is to defeat and ultimately destroy ISIL,” General Austin said. “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.”

As the militants have been put on the defensive over the last few days, the number of airstrikes has decreased. American military officials said they had conducted six airstrikes in Kobani on Thursday and Friday, a sharp decline from the 37 attacks carried out over a three-day period earlier in the week.

“ISIS is retreating and we are advancing,” said a commander serving with a unit of Syrian antigovernment rebels who have allied themselves with the Kurds.

“Airstrikes destroyed most of their heavy weapons,” said the commander, who uses the nom de guerre Abu Hasan. The militants had also lost their supply lines and were no longer able to move freely in and out of the city. “Those who are left in the city center don’t have a way out,” he added.

Abu Hasan and his fighters chased a group of militants to a hill about three miles west of Kobani, overrunning their position with the help of airstrikes. He said that his unit had not been able to advance farther because of sniper fire, but that he did not expect the resistance to last long.

“We caused ISIS losses in equipment and souls,” he said. “The battle will be ending soon.”

Signs of the toll on the militants began to emerge Friday. A video apparently taken by Kurdish fighters showed the aftermath of an airstrike: In the midst of collapsed buildings and pulverized vehicles, the fighters walked among body parts as they toured the razed site.

On a cellphone purportedly captured from a dead Islamic State fighter, voice messages sent to a friend, according to a rebel media activist who heard them, revealed the sudden swing of the battle: from supreme confidence that the capture of Kobani would take 10 days to laments as the militants were surrounded by Kurdish fighters, who had “popped up” everywhere.

“All of my group is killed now, and I’m left alone here,” the activist quoted the militant as saying.

As Kobani braced for any regrouping by the Islamic State, Kurdish and rebel fighters took advantage of the calm. Ahmed Bouzi, a 21-year-old fighter who had sneaked out of Kobani to buy medicine in Turkey, marveled at the shift from just weeks ago, when he and 50 others were retreating under fire as what felt like thousands of militants closed in on them.

Now, “they are retreating, slowly,” Mr. Bouzi said before heading back to Kobani, just in case.