By the end of the first day of the highly anticipated offensive for the Iraqi city of Mosul, there were two wars—the one on the battlefield and the one fought in words by officials seeking to shape the most important battle ever against the self-proclaimed Islamic State.

On Monday, some officials were eager to promote that even as ISIS had slowed ground troop advances with mortar fire and smoke billowing from burned oil fields, its loss was inevitable.

Iraqi officials reportedly said they reclaimed 17 villages. The U.S. repeatedly insisted the Iraqis are in the lead, even as they privately conceded that the fight for Mosul could put U.S. troops in harm’s way.

And as the day’s fighting subsided, Kurdish leaders said that despite past tensions, Arab and Kurd forces would find common ground through this battle.

“This is the first time the blood of the Peshmerga and the Iraqi forces are mixed. We hope it’s a good start to create a bright future for both sides,” Masoud Barzani, president of the Kurdistan region, said Monday.

Meanwhile, at the Pentagon, spokesman Peter Cook said Day 1 of the campaign was “ahead of schedule” but did not say how. A U.S. defense official told The Daily Beast that Iraqi and Kurdish forces expected to meet more resistance than they did. Some defense officials suggested that while they were happy with Monday’s outcome, they would not be ready to celebrate until Iraqi and Kurdish forces had moved into the city center, which would be the ultimate metric of ISIS’s willingness to fight for the Iraqi capital of its so-called caliphate.

Together, Arab and Kurdish forces make up at least 45,000 troops—and as many as 80,000—that are confronting an estimated 5,000 ISIS fighters in Mosul, according to U.S. estimates. The U.S.-led coalition also is conducting airstrikes on behalf of Iraqi and Kurdish Peshmerga forces, including four such strikes Monday, according to a coalition press release.

Several hundred U.S. ground forces are at headquarters in the back of the frontline troops, defense officials said, advising and giving local forces intelligence, forward air controllers, and other support. So far, those forces have remained behind the front line, defense officials said, staying with the headquarters units that are the caboose of the Iraqi Special Forces moving north toward Mosul and Kurdish forces moving westward.

It remains unclear, however, U.S. officials said, how much risk U.S. forces will face in what could be a months-long battle for Mosul. Could U.S. forces enter Mosul, alongside their Iraqi counterparts? Speaking before reporters Monday Cook at first said it was possible, noting he did not want to rule anything in or out. Later he said:

“Americans are again playing an adviser role, an enabler role for these Iraqi forces… Most of the American forces in Iraq are not anywhere close to the front line. The role of the US forces today is no different than up to this point” of the two-year U.S. involvement in Iraq supporting the fight against ISIS.

Even before the battle for Mosul began, there has been a general sense of inevitability about the outcome in favor of the Iraqi and Peshmerga forces. The worry is about what happens after, when the spoils of the largely Sunni and Kurd oil-rich city are divided among the Shiite-led government, the Shiite militias that are joining the battle, the Iraqi forces, the Peshmerga, and states like Turkey and Iran, which has played a role in the battle against ISIS.

Perhaps because of that, some are trying to shape the outcome even before it happens through rhetoric, hoping today’s words will mitigate tensions in post-ISIS Mosul.

Cook said that in the next two days, the coalition would be dropping 7 million leaflets for the roughly 1 million civilians trapped in Mosul, urging them to stay inside and hunker down such that they are not confused with ISIS fighters. U.S. officials said they were not aware of any Kurdish or Arab force deaths, or civilian casualties, during the first day of fighting.

Mosul, Iraq’s second-largest city, fell under ISIS control June 10, 2014, when the terror group easily claimed the city as Iraqi forces shed their uniforms and fled. Wresting Mosul from ISIS would effectively mark the end of the group inside Iraq, as it has lost control of nearly every Iraqi city once under its control, including Fallujah, Ramadi, Baiji, Tikrit, and Hit.

The only place left for ISIS to flee, should Mosul fall, is the nearby city of Hawijah. So far, officials said, there is no indication that ISIS fighters have fled there since the operation began.

“We will know in the next few days how much they are willing to fight,” one defense official concluded.