As many as 7,000 ISIL fighters and active supporters remain in Iraq after the fall of Mosul, according to high-ranking Iraqi security officials.
Three intelligence and defence officials said there were an estimated 4,000 militants and 3,000 supporters who were employed by the group and received salaries.
In Syria, there are up to another 7,000 militants and 5,000 supporters, they said.
Mosul, ISIL's largest urban stronghold in Iraq, was declared liberated from the extremist group on July 10 after nine months of highly destructive warfare.
Two days later the commander of the US-led coalition against ISIL, Lt Gen Stephen Townsend, cautioned that the battle was not over. He said Iraqi troops needed more time to oust remaining ISIL fighters from Mosul.
He said they would then probably take a break to regroup before launching their fight against ISIL in Tal Afar and other remaining insurgent strongholds in western Iraq. ISIL still controls territory in parts of Nineveh and Anbar governorates, in Hawija in Kirkuk province and in pockets elsewhere.
The extremists conquered much of northern and western Iraq after sweeping into Mosul June 2014. The group then declared a caliphate in Iraq and Syria and governed according to a harsh and violent interpretation of Islamic law. The militants rounded up their opponents and killed them en masse, often documenting the massacres with video and photos.
Last week, Nick Rasmussen, director of the US National Counterterrorism Centre, warned that the world still faced threats from ISIL despite its territorial losses. He said the group controlled less territory, but officials werel worried that a small number of skilled fighters could move out of the region and launch attacks in the west or in their homelands.
In Syria's Raqqa, ISIL's self-proclaimed capital, US-backed Syrian forces encircled the city, breached fortified defences and moved closer to its centre. Officials predict a long, tough battle, estimating that more than 2,000 militants are holding out there with their families and tens of thousands of civilians.
Last summer, the Pentagon claimed the military campaigns in Iraq and Syria had taken 45,000 enemy combatants off the battlefield and reduced the total number of ISIL fighters to about 15,000. In March, Lt Gen Townsend said US intelligence estimates put the number of ISIL fighters in Iraq and Syria combined at 12,000 to 15,000. That was down from an estimate of 19,000 to 25,000 in February 2016 and 20,000 to 31,000 in 2014.
Iraqi intelligence officials said ISIL leader Abu Bakr Al Baghdadi was still alive, despite several reports that he had been killed.
"We will be reviving ISIL if we killed Baghdadi now," one of the top officials said, adding that the strategy was to get rid of possible successors first. "We want to cripple the group in order to end it. We don't want to give them a window for a comeback."
There have been conflicting reports of Al Baghdadi's death, including a claim by Moscow in late May that there was a "high probability" he was killed in a Russian airstrike in the southern outskirts of Raqqa.
Lt Gen Townsend has said he does not know whether Al Baghdadi is dead or alive.
"I suppose it probably doesn't really matter. If no one knows if he's alive or dead, someone is guiding ISIL, the organisation," he said. "And what we have seen with all these paramount leaders is you take them out, and someone else steps up."
