David Cameron has vowed that Islamic State (Isis) will "be squeezed out of existence", and promised to build a coalition in the region against it that cannot be mistaken for a western-led intervention.

His remarks appeared to be preparing the ground for a broad coalition that includes Britain, to drive out Isis following a formal invitation from the Iraqi government in Baghdad.

Whitehall sources suggested that planned air attacks on Isis forces based in Syria will be deferred, partly because it would involve incursions into Syrian air space without any invitation from its government. That would change the legal status of any attacks and possibly weaken the potential regional coalition.

Cameron sidestepped the issue of attacks on Syria when pressed by the former Labour cabinet member Peter Hain. Details of the scale of the coalition response are likely to be hammered out at Nato's meeting in Newport, Wales, over the next three days, including a meeting of the five leading Nato powers on Friday morning.

Vowing the country will never give into terrorism, the prime minister also braced the population for further potential bad news about the British hostage.

He warned: "I think what has happened to the two hostages so far and what may happen again in the future is utterly abhorrent and barbaric. These people need to understand we will not waver in the our aim of defeating terrorism."

Cameron's tone and language echoed that of Barack Obama, who vowed on Wednesday that the US will not be "intimidated" by the beheading of the American journalist Steven Sotloff. Speaking in Estonia on the way to the Nato summit, Obama said: "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."

Cameron vowed the UK would not pay ransom to terrorist kidnappers. He said: "We should see this crisis as one where we are there to help the people on the ground and the countries in the region that want to solve this crisis.

"We should not see this as one where it is somehow a western-led intervention. We have the Kurds who are defending communities, including minority communities, from the horrors of Isil [Isis].

"We have the government in Baghdad, which badly needs to get itself together so it can represent all of the country and then we, with allies and neighbours, can do more to make sure this appalling organisation Isil feels the full pressure of international and regional and local condemnation.

"We should be using all the assets that we have, focusing first on humanitarian aid and saving people from persecution, hunger and starvation, using our diplomatic and political pressures to make sure there is a government in Baghdad that can represent all of the country, and marshalling, working with others, so the maximum pressure is put on.

"If we continue in that way, always asking ourselves how can others in the neighbourhood do their work, how can we help them, and how do we best defend our national interest and keep our people safe at home, that is the right approach."

He added: "It is not enough to target those who preach violent extremism – we need to go after those that promote the extremist narrative and life view that gives the terrorists and the men of violence support for what they do.

"It is not unlike the cold war, where we did not just pursue those who wanted to do us such harm, we also had to challenge all those who gave them succour."

Cameron's broad strategy, including a full debate next Wednesday, won the unconditional support of the Labour leader, Ed Miliband, although Miliband urged him to involve the UN and is critical about the coherence of the plans for domestic legislation. The Labour leader said there is "a pattern of murderous behaviour by Isil of the innocent. Christians, Yazidis, Muslims, anyone who does not agree with their vile ideology.

"Events like this must strengthen, not weaken, our resolve to defeat them and you can be assured of our full support in standing firm against them."

Discussing domestic legislation to curtail jihadis travelling to Syria and Iraq, Cameron said reintroduction of relocation powers would go ahead with legislation adding urgency is the order of the day.

He also suggested his plan to block British-born jihadis returning to the UK was legal. "I do believe it is legally permissible, but it's going to require some work … of course the best thing to do is to gather evidence, prosecute and convict and imprison, but there may be occasions where we need to exclude and fill that gap in our armoury."

Cameron had opened prime ministers questions with a mini-statement saying: "I'm sure that the whole house and the whole country will join with me in condemning the sickening and brutal murder of another American hostage and share our shock and anger that it again appears to have been carried out by a British citizen. All our thoughts are with the British hostage and his family. Their ordeal is unimaginable. But let me be very clear: this country will never give in to terrorism.

"Our opposition to Isil will continue at home and abroad. It is important that we are clear about the nature of the threat we are facing. It makes no distinction between cultures, countries and religions. There is no way to appease it. The only way to defeat it is to stand firm and to send a very straightforward message: a country like ours will not be cowed by these barbaric killers. If they think that we will weaken in the face of their threats, they are wrong. It will have the opposite effect."