The Kurdish recapture of Kobani in northern Syria appears to have provided a blueprint for defeating the Islamic State, bringing together U.S. air power with an effective ground force and protected routes for the movement of fighters and weaponry. Taking back the key Iraqi city of Mosul may be an entirely different matter.

As Kurdish fighters, buoyed by their success after months of fighting near Syria's Turkish border, expanded their offensive Tuesday, American officials were able to point at long last to a victory in the battle against the Islamic State. The takeover of Kobani, which the U.S. says is now 90 percent complete, has put the extremists on the defensive.

U.S. efforts were part of the story.

American air strikes killed more than 1,000 Islamic State members in and around Kobani, including major figures in the militia's command structure and many of its most battle-hardened fighters, a senior State Department official said. Kurdish peshmerga forces and Syrian rebels were able to reverse momentum on the ground by reaching Kobani through Turkey, a corridor established after much U.S.-Turkish diplomacy.

Similar efforts are occurring right now in Iraq, said the official, who briefed reporters on condition he not be quoted by name. He cited operations in the western Iraqi town of Haditha, where local tribes and Iraqi forces have slowed the Islamic State's advances across a Sunni-dominated area of the country.

But the official suggested a coordinated offensive in Mosul, an Iraqi city of a million people and the scene of the militant group's greatest military triumph, may not happen imminently — despite widespread speculation to the contrary.

The Islamic State "wants to draw security forces into a prolonged, urban, street-by-street combat," the official said. "We're not going to fall for that."

Instead, the official described a more methodical effort to "squeeze" the insurgency in Mosul, pointing to recent Iraqi successes along the main supply route between the city and the Islamic State's power base in northern Syria.

The battle "will be on our timeline; it will be on the Iraqi timeline," the official said. He said the U.S. was helping to train local police who were chased out of Mosul last year so that they could serve as a stabilization force once it is retaken.

Any Mosul operation is likely to be far more elaborate than Kobani, which doesn't seem to have involved much effort toward rooting out the ideology that has fueled the Islamic State's war effort and made it popular across the Arab world.

For Mosul, the U.S. will likely spend far more time honing a counterinsurgency strategy that seeks security for the city's inhabitants and reinforces loyalty with the Iraqi government. Otherwise, locals may welcome militants back after the bombings end, a sequence that has played out repeatedly in Iraq and Afghanistan over the last decade.

"Eventually there's going to have to be a fight for Mosul. We know that," said Rear Adm. John Kirby, the Pentagon spokesman. But he said the U.S. was still working with Iraqi forces to "better understand the challenges" and make them "as battlefield-competent as possible."

Amid the Islamic State's rapid advance across much of Syria and Iraq last year, Kobani was originally an afterthought for the U.S. It emerged as a potential turning point almost accidentally.

In September, Islamic State fighters captured about 300 Kurdish villages and hamlets nearby and then thrust into the town itself, occupying almost half of it and sending tens of thousands of residents fleeing into Turkey. Unsure if Kobani would hold, U.S. officials including Secretary of State John Kerry spent weeks saying the town wasn't a U.S. priority.

But as Islamic State fighters poured north from their main control point in the Syrian city of Raqqa, they exposed themselves to air strikes as part of the broader U.S. military effort to weaken the group's capabilities. Humanitarian airdrops then started in late October, with Turkey helping Kurdish reinforcements arrive thereafter.

Holding Kobani means keeping a long stretch of the Turkish-Syrian border out of the Islamic State's hands. Perhaps just as importantly, the Obama administration sees the defeat challenging one of the group's main draws for would-be foreign fighters from across the Muslim world and from the West: its self-projection as a triumphal movement rolling from victory to victory.

The senior State Department official said there have been reports of increased "fratricide" among Islamic State fighters, with dozens recently being killed for refusing to fight.