WASHINGTON » The Islamic State is facing growing dissension among its rank-and-file fighters and struggling to govern towns and villages it has seized, but the militant Sunni group is still managing to launch attacks and expand its ideological reach outside of Iraq and Syria, senior U.S. officials said.

In the seven months since allied warplanes in the U.S.-led air campaign began bombing select Islamic State targets, the Sunni militancy, while marginally weaker, has held its own, senior defense and intelligence officials said.

Even after the Islamic State lost much of the central Iraqi city of Tikrit, following more than a week of fierce fighting, Pentagon officials warned that it would be as difficult for Iraqi forces to hold the city as it was to liberate it. The Islamic State fighters were, in the meantime, mounting one of the fiercest assaults in months in the city of Ramadi, west of Baghdad.

But tensions have become apparent inside the Islamic State, also known as ISIS, ISIL and Daesh. The troubles stem from new military and financial pressures and from the growing pains of a largely decentralized organization trying to hold together what it views as a nascent state while integrating thousands of foreign fighters with Iraqi and Syrian militants.

The tensions were described in recent interviews with a Syrian fighter who recently defected from the group and an Islamic State recruiter who still works with the group, but is critical of some of its practices. The troubles were consistent with accounts from residents of areas that the Islamic State controls and from interviews with numerous Syrian activists who oppose both the Islamic State and the Syrian government. Those activists have recently fled from those areas, but maintain extensive contacts there.

There are reports of dozens of executions and imprisonments of Islamic State fighters trying to flee the group. There are strains in fighting on multiple fronts, with some fighters being deployed to battles that, they complain, are not strategically important. There are complaints about salaries and living conditions, disputes over money and business opportunities, and allegations that commanders have left with looted cash and other resources.

And there is growing anecdotal evidence that some members of the group — particularly locals who may have joined out of opportunism or a sense that it was the best way to survive — have been repulsed by its extreme violence.

"I still feel sick," Abu Khadija, the Syrian defector, said recently after witnessing what he said were the beheadings of 38 Kurdish and Alawite war prisoners by Islamic State fighters in Yaroubiyeh, a Syrian town on the Iraqi border. Abu Khadija asked to be identified only by his nickname for his safety.

Despite such accounts, Gen. Lloyd J. Austin III, the head of U.S. Central Command, said the battle against the Islamic State is nowhere near won. Although Austin told the U.S. House Armed Services Committee last week that airstrikes have killed more than 8,500 militants, eliminated the group’s primary source of oil revenue and hurt the ability of its leaders to command and control its troops, Pentagon and counterterrorism officials said the militant group is increasingly dangerous through new affiliates in Afghanistan, Algeria, Egypt and Libya. Boko Haram, the Islamic militant group in Nigeria, became the latest group to swear allegiance last Saturday.

The self-declared caliphate has lost only about 20 percent of the territory it seized in Iraq — most of it in the north, to Kurdish peshmerga troops who have been supported by the United States, the Iraqi government and Iran, a senior defense official said. The main areas it has lost — most of Tikrit, territory southwest of Baghdad, some of the areas to the north of the Iraqi capital and the Kurdish city of Kobani in Syria — have been the focus of the overwhelming allied air campaign.

"Other than that, we’re basically looking at what we had before," said Jessica Lewis McFate, research director with the Institute for the Study of War. "Their numbers are reduced, but their foreign fighter flows are still robust."

Obama administration officials also said they faced major challenges in countering the Islamic State’s propaganda machine, which pumps out as many as 90,000 Twitter messages and other social media communications every day, and is attracting about 1,000 foreign fighters a month from across Europe, North Africa, the Middle East and the United States.

"ISIL is well-armed and well-financed," John Brennan, the CIA director, said in a speech Friday at the Council on Foreign Relations in New York. "ISIL will not be rolled back overnight."

Despite the air superiority that the U.S. coalition commands in the skies above Iraq, in late January hundreds of Islamic State gunmen mobilized an attack on Kirkuk, the oil-rich Kurdish city that thus far has been protected by peshmerga forces. Militants temporarily seized an abandoned hotel that the local police had used as their headquarters. Suicide bombers detonated their explosives to keep Kurdish forces at bay, and militants took over an area southwest of Kirkuk after heavy clashes with Kurdish forces.

Although the Kirkuk attack was ultimately unsuccessful, the group still has control of the largest territory ever held by a terrorist group, Nicholas Rasmussen, the director of the National Counterterrorism Center, told a Senate committee last month. "This safe haven provides ISIL and other extremists with the time and space they need to train fighters and to plan operations," Rasmussen said.

Abu Khadija, the defector who witnessed the 38 beheadings, said he was trying to get into Turkey, despite knowing that Islamic State militants might kill him if they caught him. He said he could not forget the beheadings.

"I can’t eat. I feel I want to throw up. I hate myself," he said, adding that the executioners had argued over who would wield the knives and finally settled the issue by lottery. "Honestly, I will never do it. I can kill a man in battle, but I can’t cut a human being’s head with a knife or a sword."

During nearly a year in contact with New York Times reporters, Abu Khadija expressed gradually growing discontent. His grievances ranged from relatively mundane issues like eating canned food and being deployed to a front line far from his family because of a lack of fighters, to discomfort with the group’s strategic priorities and its extreme violence.

Such defections, according to an increasing number of reports, are not isolated cases. In Iraq on Monday, residents of the northern town of Hawija, requesting anonymity for their safety, said that dozens of Islamic State fighters were executed by their comrades for trying to flee the front as the group came under attack from Kurdish peshmerga forces.

Overall, there has always been mistrust between Syrians and foreigners in the Islamic State, said Omar Abu Layla, a longtime activist in Deir al-Zour who is now in Germany and tracks jihadist groups through contacts back home, and uses a nom de guerre for his contacts’ safety.

Islamic State foreign fighters, known as muhajireen, dominate the group’s military leadership and administrative bureaucracy, according to Abu Layla. "The mistrust was obvious from the beginning," he said. "They never trusted the locals."

© 2015 The New York Times Company