High-ranking Iraqi security officials said up to 7,000 affiliates to the militant Islamic State group (IS) group remained in Iraq after the fall of Mosul, where the group's leader declared the self-styled caliphate three years ago.

Three intelligence and defense officials told The Associated Press there are an estimated 4,000 militants and 3,000 supporters in Iraq, who were employed by the group and received salaries. In Syria, there are up to another 7,000 IS militants and 5,000 supporters, they say.

The officials spoke to the AP on condition of anonymity because they are not authorised to speak to the media.

On July 10, Iraq's Prime Minister Haider al-Abadi declared the liberation of Mosul, after nine months of highly destructive warfare.

The IS swept into Mosul in summer 2014 when it conquered much of northern and western Iraq. The extremists declared a caliphate 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.

Two days after the declaration of Mosul liberation, Army Lt Gen Stephen Townsend, commander of the United States led coalition in Iraq and Syria, cautioned that the battle in Iraq is not over. He said he believes Iraqi troops still need time to oust remaining IS fighters from Mosul.

Once that is done, he said, they will probably take a break to regroup before launching their fight against the IS in Tal Afar and other remaining insurgent strongholds in western Iraq.

The IS still controls territories in parts of Ninawa and Anbar governorates, in Hawija in Kirkuk governorate and in pockets elsewhere.

Last week, Nick Rasmussen, director of the National Counterterrorism Center, warned that the world still faces threats from IS militants despite their territorial losses. He said the IS group controls less territory, but officials still worry 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, IS's self-proclaimed capital, the US-backed Syrian forces encircled the city, breaching the fortified defenses and moving closer to the heart of the city. Officials are predicting a long, tough battle, estimating that more than 2,000 militants are holed up with their families and tens of thousands of civilians in the city's centre.

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 IS fighters to about 15,000.

In March, Lt Gen Stephen Townsend, commander of the US-led coalition forces in Iraq and Syria, said the US intelligence estimates put the number of IS 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.

Amid reports that IS leader Abu Bakr al-Baghdadi was killed, Iraqi intelligence officials told The Associated Press that he is still alive.

“We will be reviving ISIS if we killed Baghdadi now,” one of the top officials said, adding that the strategy is 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. Townsend earlier said he doesn't know if he 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 ISIS, the organisation,” Townsend said.

“And what we have seen with all these paramount leaders is you take them out, and someone else steps up.“