Barack Obama and David Cameron have vowed to use the Nato summit starting in Wales on Thursday to engineer a resilient military and political coalition, including key countries in the Middle East, capable of squeezing out and destroying Islamic State (Isis) in northern Iraq.

British officials also said the Britishprime minister was examining every option to protect the British hostage threatened by the jihadist group on Tuesday, in light of its murder of the American journalists Steven Sotloff and James Foley in the past month.

"We will not be intimidated," Obama said in Estonia on the way to the summit. "Their horrific acts only unite us and stiffen our resolve to take the fight against these terrorists. And those who make the mistake of harming Americans will learn that we will not forget and that our reach is long and that justice will be served."

The British hostage, whose identity has been widely circulated in international media, is a 44-year-old aid worker, David Haines, who was kidnapped in March last year and shown in the video of Sotloff's murder. He was taken hostage in the village of Atmeh in Syria's Idlib province along with an Italian aid worker and two Syrians. The others have since been freed.

The British foreign secretary, Philip Hammond, admitted that an attempt to rescue Haines earlier this year failed and that current British intelligence on his whereabouts is limited.

Obama, under intense domestic pressure to set out his strategy for dealing with Islamic State, pleaded for patience to build support in the region, saying: "It is going to take time for us to form the regional coalition that's going to be required so that we can reach out to Sunni tribes in some of the areas that Isis has occupied, and make sure that we have allies on the ground in combination with the air strikes that we've already conducted."

Officials in Washington and London said that in building an international coalition against Isis, they were following the approach of the first President George Bush, who assembled a broad-based coalition before throwing Saddam Hussein out of Kuwait in 1991.

Obama said: "We know that if we are joined by the international community, we can continue to shrink [Isis's] sphere of influence, its effectiveness, its financing, its military capabilities to the point where it is a manageable problem. And the question is going to be making sure we've got the right strategy, but also making sure we've got the international will to do it."

UK prime minister David Cameron on the eve of the Nato summit. Photograph: Ben Gurr/AFP/Getty Images

Cameron, arriving at the Nato summit , said he was weighing the options of joining the existing round of US air strikes in Iraq: "We should do what we can to help those on the ground who want to build an Iraq for all Iraqis: Sunnis, Shias and Kurds. We've helped already with aid.

"We've helped with other military assets, and we'll always ask ourselves what is in our national interest. Not ruling things out, but going forward in a deliberate, sensible, resolute way." It is clear Cameron is edging towards direct British involvement in the US air strikes, even though it may make Haines more vulnerable to the kind of gruesome murder inflicted on the two American journalists.

Cameron, at weekly prime minister's questions, did not flinch from referring to the possibility of Haines's death, and insisted Britain would not be deterred by threats of thefrom Isis, or pay a ransom. He said: "A country like ours will not be cowed by these barbaric killers. If they think we will weaken in the face of their threats, they are wrong."

But in Cameron's key message, reflecting thinking in Washington, he said any intervention in Iraq must not be western-led, and be at the invitation of the Iraqi government. The Turkish president, Recep Tayyip Erdogan, and the Jordanian king, King Abdullah, will be at the summit, and both will be courted to support tougher military action against Isis. Jordan's participation at the summit will be of "immeasurable illumination" of the strategy of confronting Isis, the British ambassador to Jordan, Peter Millett, has said. There is also intense pressure on Saudi Arabia to recognise that its funding of Sunni forces in Syria has helped spawn Isis.

Some former Labour cabinet members went even further, suggesting America and Britain should make common cause with its long time foes Iran and even the Syrian President Assad so as push Isisnot just out of Iraq, but its original base Syria.

In a joint article published in the Times, Cameron and Obama say Britain and the US can lead efforts to secure world peace. "If terrorists think we will weaken in the face of their threats, they could not be more wrong. Countries like Britain and America will not be cowed by barbaric killers … We will be more forthright in the defence of our values, not least because a world of greater freedom is a fundamental part of how we keep our own people safe." They also accuse Vladimir Putin of "trying to force a sovereign state to abandon its right to democracy and determining the course of [Ukraine's] future at the barrel of a gun" and write that "we must increase Ukraine's capacity to defend itself".

In a packed Nato agenda, Cameron and Obama will hold a bilateral meeting focusing on the Middle East. It is possible Nato will send a training mission to Iraq.

John Kerry, the US secretary of state, will travel to the Middle East after the summit to gather further regional support. Kerry has cited the Bush-era coalition-building of his predecessor, James Baker, concluding that "extremists are defeated only when responsible nations and their peoples unite to oppose them".

Obama, criticised last week for saying the US "did not have a strategy" to defeat Isis in Iraq and Syria, also gradually expanded his military objectives, saying the aim was to degrade and destroy Isis, rather than just to protect US citizens and vulnerable minorities.

The US vice-president, Joe Biden, ramped up the rhetoric by saying the US would follow those who killed the two American journalists "to the gates of hell".

Cameron also revived his plans to withdraw citizenship from British-born jihadists who go to fight in Syria and Iraq and then seek to return to Britain. "People across our country take the basic view that if someone leaves this country, travels to the heart of Iraq, declares they are in favour of some so-called Islamic state, and that is the country they want to be part of, they should effectively forfeit their right to come back and live in Britain," he said.