Barack Obama hailed the formation of a "core coalition" of 10 countries – led by the United States and including the UK, France and Australia – who were aiming to destroy what he described as the savage and nihilistic Islamic State (Isis) in Syria and Iraq.

Speaking at the closing of the Nato summit in Wales, the US president said the grouping, which also included Germany and Canada, "stood ready to confront this terrorist threat with military, intelligence, law enforcement as well as diplomatic efforts".

But the core coalition only included one Muslim nation, Turkey. The US secretary of state, John Kerry, will now travel to the Middle East to build support for a military confrontation with Isis, an organisation that Obama said "killed innocents and enslaved women".

Intent on learning the lessons of the 2003 Iraq invasion, led by George W Bush in conjunction with Tony Blair, Obama added that it was absolutely critical that "we have Arab states – and specifically Sunni majority states – prepared to join the fight".

David Cameron, speaking at the close of the Nato summit, also gave his clearest commitment to British military involvement saying a "military commitment was required, but the government was not at the stage of making decisions on air strikes".

In his own post-summit press conference, the UK prime minister said what was needed was a combination of "intelligent politics, diplomatic pressure, long-term engagement in a comprehensive plan, as well as the potential for military, or other aggressive action".

The aim of the grouping will be to corral as many Middle Eastern countries into the coalition ahead of a meeting of the UN security council hosted by Obama in the week of 22 September in New York. Cameron is expected to attend the meeting.

Kerry also promised that the US would aim to win broad support to defeat Isis at the UN General Assembly later in the month. It is not yet clear if the US will table a resolution seeking legal backing for the use of force and whether this will extend to Syria, the birthplace of Isis.

Cameron will give a Commons statement on Monday and attend a full day debate on Wednesday that will give government whips a chance to gauge political support for British involvement including air strikes and special operations. The prime minister was upended last year when he failed to foresee opposition to air strikes in Syria to punish Assad for his use of chemical weapons.

On the question of whether it would be necessary to secure UN support for any deeper military action, an issue certain to be raised by Labour leader, Ed Miliband, the prime minister was evasive, saying: "The more the UN can say to back and support hopefully a new Iraqi government in its work and to condemn Islamist extremism the better."

The rapidly moving events show that, after weeks of internal deliberation and criticism for failing to have a clear strategy, the Obama administration clearly believe they have a diplomatic military and political plan to degrade and destroy Isis, even if in Kerry's view it may take as long as two three years to achieve.

Both Cameron and Obama said it remained their long-term intention to drive Isis from Syria by supporting moderate rebel forces in the country that Obama admitted had been out-gunned in recent months.

British sources stressed military action was not imminent, saying Obama would not step up a gear until a new stable and plural government had been formed in Iraq. It is assumed that Britain and France, with bases in the area, would offer air support.

The short-term focus will remain Iraq, with sources indicating that no attack on Isis in Syria would be considered until more had been done to identify military targets, clarify legalities and build diplomatic support for a measure that risked strengthening Syria's president, Bashar al-Assad.

Both leaders said a precondition of greater military help will be the establishment of a non-sectarian, broad-based government in Baghdad, something that is due to be achieved by the end of next week. Obama also conceded his methodical and sustained plan to drive out Isis and narrow their territory will require a stronger Iraqi army, and not just American-led air firepower.

The US president said: "The problem is that we have not seen as effective a fighting force from Iraqi security forces as we need and we are going to have to focus on the capable forces that there are and bolster them from the air, but ultimately we are going to need a strong ground game."

The aim, Obama added, was "initially to push [Isis] back, systematically degrade their capabilities, narrow their scope, slowly shrink the space they control, take out their leadership so over time they are not able to conduct the same terrorist attacks as they once could".

Cameron and Obama have both made clear they do not support forming an unholy alliance with Assad against Isis, saying Assad is part of the problem and not part of the solution. Speaking about Syria, Obama said: "We are going to have to find effective partners on the ground to push back against [Isis]. The moderate coalition is one that we can work with. They have to some degree been out gunned and out manned so we need to support them more effectively".

The 10 nations in the core coalition – first announced by Kerry – are the US, Britain, France, Germany, Canada, Australia, Turkey, Italy, Poland and Denmark. British sources did not share the phrase core coalition since the UK has been stressing this must not be seen as a western-led intervention but something that springs from Iraq and the wider Arab region, including Qatar, Saudi Arabia, Jordan, Turkey and even Iran. There are even signs that Washington is willing to co-ordinate with the Iranians to ensure there is no inadvertent clash as they put the squeeze on Isis.

But military action is already ongoing – the US has launched more than 100 air strikes on Isis positions in northern Iraq in the past month to try to contain the progress of the militants, who have seized a vast swathe of Syria and Iraq.

Kerry said there would be many ways to take the fight to Isis. US officials cited the valuable expertise of America's allies such as British and Australian special operations, Jordanian intelligence, Turkish border control and Saudi Arabia's ability to cut off financing to radicals.

Kerry stressed the length of the commitment necessary. "We have the ability to destroy [Isis]. It may take a year, it may take two years, may take three years, but we are determined it has to happen. The effort to destroy and degrade [Isis] will take time and persistence".

He said Friday's initiative proved: "We have the ability to come together, that our capacities of defence are not frozen in an old model that we cannot respond to something like this."

Philip Hammond, the British foreign secretary, who chaired the meeting with Kerry, said: "It's going to be a long campaign; not necessarily a military one, but a campaign to turn the tide, to cut off the funding, to undermine the recruiting, to cut off the support that they're receiving from some of the countries around the world and to push [them] back.

Nato also announced it would offer to build defence capacity in Iraq if requested by the new non-sectarian government due to be formed by the end of next week. The secretary general, Anders Fogh Rasmussen, said Nato would also co-ordinate the humanitarian airlift in Iraq as well as an information exchange on jihadi fighters returning to their home countries.

In a sign of early support from the Middle East, the United Arab Emirates foreign ministry released an unusually strong statement condemning the atrocities committed by Isis.