Dramatically weakened on the ground, the Islamic State group faces military defeat in its one-time "caliphate" -- but experts say it is almost impossible to know how many members it still has.

Online, IS propaganda claims it is undefeated in what's left of its territory -- a small patch of eastern Syria -- which is a fraction of the land it once controlled spanning the war-wracked country and neighbouring Iraq.

Claims of responsibility for deadly attacks in Syria as well as disparate acts of violence, such as Thursday's stabbings near Paris, are intended to keep the organisation in the news.

But experts tracking the jihadist group's every move cannot agree on how many active members it still has, not least because much of its former territory remains an inaccessible warzone.

The Soufan Group, a security consultancy, noted that in December the US-led coalition had estimated the number of IS fighters across Iraq and Syria at 1,000.

Last week, in contrast, the US Defense Department estimated there could be up to 17,000 left in Iraq and 14,000 in Syria.

United Nations observers gave yet another estimate in a recent report -- somewhere between 20,000 and 30,000 between Iraq and Syria.

"The wild swings in estimates have been a hallmark of the anti-IS campaign since its inception in 2014," the Soufan Group said.

Spawned from Islamist movements present in Iraq for years, IS' ranks were quickly swelled by volunteer fighters, arriving first from around the Middle East and then the world.

Since the foreign fighters arrived via clandestine border crossings, international intelligence agencies have always had to make do with estimates.

- Bodies under the rubble -

"Today, the main pitfall in reaching a trustworthy figure is that we do not know how many among their ranks have been killed in coalition operations, Russian operations, Iraqi or Turkish operations," said French terror expert Jean-Charles Brisard.

"The bodies of jihadists killed in these air raids are in many cases still under the rubble -- no one will find them," said Brisard, head of the Center for the Analysis of Terrorism (CAT).

"So, until we know for sure that they have been killed, they're considered to be still alive. Some are even still taken to court in absentia."

Tore Hamming, an expert on Islamic extremism at the European University Institute, an academic centre in Italy, believes the UN estimate is much too generous to the jihadists.

"I don't believe the numbers, but I also think it is impossible to assess," he said.

"First you need to define what an IS fighter or member is.... back in 2015 some spoke of IS being a 200,000-strong force because they included people working in the IS administration," he added.

"The new number, does that only cover people with a gun, or everybody working for the cause of IS? Nobody knows."

Another factor in the uncertainty, Brisard said, is that the border between Turkey and Syria remains porous.

Turkey has reinforced its borders since the Syrian war began in 2011, but IS continues to use local smugglers to help fighters to cross it.

"Many jihadists have crossed illegally into Turkey and are still there, waiting to be able to go to another area where (IS) is operating," Brisard said.

"The precise numbers will remain uncertain. All that we know is that there are redeployments towards other places -- Pakistan, Afghanistan, the Philippines."

As IS shifts towards a strategy of encouraging lone-wolf attacks, the Soufan Group said it had "slipped from a proto-state back to an insurgent group".

Yet it added: "It remains among the most powerful terrorist groups in history, with no shortage of weapons or willing recruits."

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US 'confident' master Qaeda bombmaker killed: official
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