For the coalition to work, the US needs help from neighbours of Iraq and Syria, and those with influence in the region

When George W Bush announced "a coalition of the willing" in the run-up to the invasion of Iraq in 2003 it was met with widespread derision. This was partly because of its composition, scraped together from around the world but without the backing of Arab and Muslim leaders.

It is unfortunate, then, that John Kerry, the US secretary of state, used the near identical phrase on the sidelines of the Nato summit in Newport on Friday when he described the alliance of countries prepared to take on Islamic State (Isis), which controls swathes of Iraq and Syria, as a "coalition of the clearly willing".

There was a wince from European and US officials, because Barack Obama's coalition is facing exactly the same problem. For the coalition to work, the US needs the help of the countries neighbouring Iraq and Syria, and those with influence in the region. The "core group", of the US, UK, France, Germany, Turkey, Italy, Canada, Australia and Poland, has no Muslim country except Turkey.

The White House has expressed optimism that this will change, with Obama insisting that there would be regional backing for the coalition. Kerry is set to head a delegation to the region to rally allies. "Countries that don't have a lot in common and countries that don't always co-operate with us are starting to stand up," Tony Blinken, the US deputy national security adviser, said on Friday in an interview with MSNBC.

But is it possible to persuade long-term foes to lay aside differences? Will Shia-dominated Iran, which has influence over the governments in Baghdad and Damascus, collaborate with Sunni-dominated Saudi Arabia?

Obama faced an early rebuff when he met King Abdullah of Jordan on Thursday. The king offered to help with intelligence gathering but, according to US officials, wanted Jordan to maintain a low international profile.

At the Nato gathering, Kerry spoke about a "holistic" and "kinetic" approach to the problem. There would be a "new model" for tackling this and similar international challenges. Countries would provide whatever expertise they could: air power, military training, arms exports, intelligence gathering, diplomatic efforts and law enforcement.

In practice, the US will almost certainly continue with air strikes in Iraq, having carried out more than 100 already, to prevent Isis's expansion and help Kurds and the Iraqi government regain control. The UK is considering a switch from humanitarian flights to military strikes and the Australian government said it will join in military strikes.

But military strikes alone cannot defeat the militants. Air power can stop them taking control of targets such as the vital Mosul dam but cannot dislodge them from urban areas.

Craig Whiteside, a former US infantry officer, writing in his War on the Rocks blog, warned: "The momentum for expanded air strikes against Islamic State in both Iraq and Syria is increasing, if for no other reason than that the tool is readily available and has low risk for the United States Unfortunately, the results of such a campaign will be extremely limited if they are not part and parcel of a policy that achieves a stable Iraq."

Producing a stable Iraqi government is hard to do, as the US found during its occupation, when it left behind a sectarian and Shia-dominated government in Baghdad.

America insists it will not send combat troops into Iraq. Instead, it wants to strengthen the Kurdish armed force, the peshmerga, as well as the Iraqi army. But strengthening the Kurdish army, with the UK already supplying military equipment, could speed up the creation of an independent Kurdish state and the dismemberment of Iraq.

Nato will almost certainly agree to send trainers to help build up the Iraqi army, but even if it succeeds,there is a danger of building up a Shia-dominated force, again accelerating the break-up of the country.

Obama hinted that the coalition might recruit the support of Sunni tribes, the key to US success against al-Qaida in Iraq.

US officials also spoke about superior technological expertise of the coalition and cited British and Australian special forces, who could be used to gather intelligence or help with targeting air strikes.

Perhaps even more problematic is how to deal with Isis in Syria. If the US extends its bombing raids into Syria, possibly with the support of the UK, it will be helping president Bashar al-Assad. That is why the US will seek the help of Iran in trying again to persuade its ally in Damascus to stand down in favour of another leader.

As for boots on the ground in Syria, the CIA has already helped train 4,000 members of the Free Syrian Army, the more moderate rebel group that is opposed to Assad and Isis. The US will step up such help, aiming to train a further 10,000, and look for the "coalition of the clearly willing" to help too.

The aim of the US is first to stop the Isis advance, as it seems to have done, and then squeeze it, taking out its leaders over the coming months, until it reaches a point that only remnants are left. Details of who is to do what will be discussed over the next few weeks, with the hope of a comprehensive plan by the end of September.

Kerry was sounding extremely ambitious at Nato. He downplayed Isis's strength, saying the group was "not 10ft tall. They are not as disciplined as everybody thinks".

He said the "coalition of the clearly willing" could be a new model to fight Boko Haram in Nigeria or al-Shabaab in Somalia next. But perhaps that might be premature given the scale of the challenge in the Middle East.