President Barack Obama and some administration officials have hailed recent military gains against DAESH in Iraq and Syria, but other U.S. officials and outside experts warn that the U.S.-backed air and ground campaign is far from eradicating the radical group, and could even backfire. While DAESH's defeats in Iraq and Syria have erased its image of invincibility, they threaten to give it greater legitimacy in the eyes of disaffected Sunni Muslims because Shiite and Kurdish fighters are a major part of the campaign, some U.S. intelligence officials argue. A second danger, some U.S. officials said, is that as the group loses ground in the Iraqi city of Fallujah and elsewhere, it will turn increasingly to less conventional military tactics and to directing and inspiring more attacks against "soft" targets in Europe, the United States and elsewhere. One U.S. intelligence official, who spoke on condition of anonymity, warned that in response to losing Fallujah and other cities the group likely would turn more to guerrilla tactics to disrupt efforts to restore government services. "We can expect DAESH to harass local forces that are holding cities it previously controlled, thereby drawing out battles into protracted campaigns," he said. The territory held by DAESH has enabled it to build up revenues through oil and taxes, provided it a base to launch attacks on Baghdad, and acted as a recruiting tool for foreign fighters drawn to the self-proclaimed caliphate.

President Barack Obama said on June 14, two days after a gunman pledging allegiance to DAESH killed 49 people in Orlando, that the militant group was losing "the money that is its lifeblood" as it continues to lose territory. Brett McGurk, the presidential envoy for the Global Coalition to Counter DAESH, told a White House briefing on June 10 that the group has lost half the territory it had seized in Iraq, about 20 percent of its self-proclaimed caliphate in Syria, and at least 30 percent of its oil production, which accounts for half its revenue. But DAESH militants in Iraq are already showing signs of adapting a guerrilla war-style strategy, Seth Jones, an analyst with the RAND Corp, told Reuters. "It looks like the areas that the DAESH has lost, they are generally abandoning, and that would mean preparing to fight another day," he said.

Despite the progress against DAESH on the battlefield and in the financial realm, CIA Director John Brennan told the Senate Intelligence Committee last week: "Our efforts have not reduced the group's terrorism capability and global reach." "The resources needed for terrorism are very modest, and the group would have to suffer even heavier losses of territory, manpower, and money for its terrorist capacity to decline significantly," he said.

Hassan Hassan, a terrorism expert at the Royal Institute of International Affairs in London, told the U.S. Senate Homeland Security committee on Tuesday that the Orlando attack showed the group's territorial losses hadn't diminished its broader appeal. "DAESH's international appeal has become untethered from its military performance on the ground," he said. Sunnis in Iraq no longer view the DAESH radicals as liberators, and the Shiite role in the fighting is less important than it was a year ago, officials in Baghdad told Reuters. As a result, they said, the Iraqi army has gained Sunni acceptance and is seen less as a Shiite-led sectarian force than it was under former Prime Minister Nouri al-Maliki. But the risk that offensives against DAESH involving Shi'ite forces could foment sectarian tensions and help the group have been underscored by allegations that 49 Sunni men were executed after surrendering to a Shiite militia supporting the army offensive to retake Fallujah. Such reports "feed into DAESH's narrative," the U.S. intelligence official said.

Iraqi forces in Fallujah are facing resistance from holdout DAESH militants in just two northern neighborhoods of the city, the operation's overall commander said on Wednesday. "The northern and central parts of Fallujah have almost been cleared of DAESH," Lieutenant General Abdulwahab al-Saadi told AFP. "There are few DAESH militants left, only in the Al-Muallemin and Jolan neighborhoods in the north of the city," he said. "The militants in Jolan are offering some resistance but we're pushing back and we've killed a number of them," he said. Operations against DAESH in northern Fallujah were being conducted by the elite counter-terrorism service and forces from the federal and provincial police.

Prime Minister Haider al-Abadi launched the offensive against the militant stronghold, 50 kilometers west of Baghdad, a month ago. After an initial phase of staging operations to encircle Fallujah, elite federal forces stormed the city center and were able to gain the upper hand relatively quickly. Abadi declared victory on June 17, saying only small pockets of DAESH fighters remained after Iraqi forces raised the national flag over the main government compound in the city center. However, the humanitarian situation becomes worse. The U.N. Security Council on Tuesday urged the international community to live up to its "moral and political obligation" to aid Iraqi civilians who fled. Council members "welcomed the successful counteroffensive" launched by Iraqi forces and coalition partners on May 22-23 to retake Fallujah, a key militant stronghold west of Baghdad that had been besieged for months. DAESH has lost 45 percent of the territory it held at the height of its strength, noted French Ambassador Francois Delattre, who holds the rotating council presidency. But more than 60,000 people have been forced from their homes in the area over the past month, and a sudden influx of civilians pouring out of the city center last week has left the aid community unable to cope.