The world's attention is on the stricken city of Kobani, in northern Syria. But for the Islamic State of Iraq and the Levant (the group known as Isis) besieging the town, it is not the Turkish borderlands but Iraq where the real thrust of its military activity currently falls.

Isis in recent weeks has won a series of victories in Iraq's Anbar province, putting a significant strategic coup within its grasp: a swath of contiguous territory stretching from its heartlands in Syria to the doorstep of Baghdad.

"It's not just about Kobani," Rear Admiral John Kirby, the Pentagon's spokesperson, said on Wednesday. "We believe that they're largely in control of the [Iraqi] town of Hit right now, which is not that far from Fallujah and Ramadi, and Fallujah and Ramadi are not that far from Baghdad. And we seem to have forgotten about that."

The Pentagon's warnings follow others that paint a somewhat dim broader picture of the current fight against the insurgency: western and Arab state air strikes against Isis appear to have reached the peak of their impact, and though Isis has been beaten back by Iraqi and Kurdish forces in some key areas in northern Iraq, its momentum appears unchallenged elsewhere.

"Isis has been advancing despite the air strikes," said Hassan Hassan, a Syria analyst at the Delma Institute in Abu Dhabi. "They have almost taken Kobani. What are we going to do when they have taken over the city? It will be an example of how the air strikes have not been working."

Isis has certainly had to adapt its tactics because of the air campaign – an effort that has already seen almost 2,000 sorties flown and 370 bombs dropped. Jihadi commanders no longer mass their troops openly, isolated military camps and bases have been abandoned in favour of urban areas, and electronic communications have been curbed, according to intelligence officials who have been building a picture of Isis's modus operandi.

But the group's core strategy appears in place.

"I see Isis doing exactly what it was doing before," says Jessica Lewis, a former US military intelligence officer in Iraq and now research director at the Institute for the Study of War. "They are showing they can absorb different types of bombardment and continue with their ground campaign – they are not laying off."

At the core of that strategy, according to Ms Lewis's research, is the consolidation of territory as both a military and socio-political objective inherent to the jihadis' narrative of creating a "caliphate".

Isis's recent, overlooked Anbar offensive is a case in point. The group has not only humiliated elite Iraqi special forces there, it has isolated them. Jihadis have surrounded Iraqi positions in Ramadi and Haditha, and they are hitting them hard with waves of truck bombs and signature blitzkrieg-style vehicle strikes. They have severed other lines of communication with Baghdad.

Most of the Euphrates valley is now within their control and if Ramadi, the last remaining centre of anti-Isis resistance, is overcome, then the jihadis will hold sway over territory from Qaim on the Syrian border right up to Abu Ghraib in Baghdad's suburbs.

It is the echo of an earlier campaign in Syria, which was also paralleled with a threatened humanitarian crisis that held the world's attention.

In August, while governments led by the US were focused on averting an impending catastrophe facing thousands of Yazidis stranded on Mount Sinjar in northern Iraq, Isis was also waging a vicious and fast campaign to wipe out all remaining resistance in Syria's ar-Raqqa governorate.

In depth Iraq crisis As lethal sectarian violence rises, the US has authorised air strikes to halt the advance of Isis Further reading

One of Isis's biggest strategic gains to date, the capture of the Tabqa air base from Bashar al-Assad's forces in late August, went almost unnoticed.

It is still far from certain whether Isis's actions fit into an overarching strategic game plan, driven by military expertise, or are merely a loosely connected series of tactical coups.

Daveed Gartenstein-Ross, director of the centre for the study of terrorist radicalisation at the Foundation for Defense of Democracies, believes that it is probably the latter.

"In Anbar, certainly, they have been tactically brilliant. But is there a co-ordinated battle plan with what is going on in Syria? What is the point in taking Kobani? To me, Isis has an extraordinarily genocidal set of political inclinations – a genocidal rage against the Kurds, and that is what has driven that."

It is, says Mr Gartenstein-Ross, a "strategic blunder".

"This is an organisation that has eyes bigger than its stomach. They are fighting on all fronts."

This, though, still gives Isis the element of surprise, and the ability to