Washington: Daesh is facing growing dissension among its rank-and-file fighters and struggling to govern towns and villages it has seized, but the terrorist group is still managing to launch attacks and expand its ideological reach outside of Iraq and Syria, senior US officials said.

In the seven months since allied warplanes in the US-led air campaign began bombing select targets, Daesh, while marginally weaker, has held its own, senior defense and intelligence officials said.

Even after Daesh 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. Daesh 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 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 a Daesh 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 Daesh controls and from interviews with numerous Syrian activists who oppose both Daesh 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 Daesh 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 Daesh 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 US Central Command, said the battle against Daesh is nowhere near won. Although Austin told the US House Armed Services Committee last week that air strikes 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 militant group in Nigeria, became the latest group to swear allegiance last Saturday.

Obama administration officials also said they faced major challenges in countering Daesh’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 (Daesh) 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(Daesh) will not be rolled back overnight.’’

Despite the air superiority that the US coalition commands in the skies above Iraq, in late January hundreds of Daesh 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.

Abu Khadija, the defector who witnessed the 38 beheadings, said he was trying to get into Turkey, despite knowing that Daesh 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.”