The UK “will not waver” in its aim to defeat terrorism, David Cameron has said as he condemned the “barbaric” beheading of a second US hostage.
Islamic State extremists threatened to kill a British hostage in a video of US journalist Steven Sotloff’s death unless US air strikes in Iraq stopped.
Ministers say “every possible option” will be considered to protect the British man. He has family in Scotland but relatives do not want him named.
IS also killed a US hostage last month.
Speaking at Prime Minister’s Questions, Mr Cameron told MPs that “this country will never give in to terrorism and our opposition to Isil (IS) will continue at home and abroad”.
“A country like ours will not be cowed by these barbaric killers”
Prime Minister David Cameron
He said: “What has happened to the two hostages so far and what may happen again in the future is utterly abhorrent and barbaric and these people need to understand we will not waver in our aim of defeating terrorism.”
An IS video posted online two weeks ago showed the killing of another US journalist, James Foley.
Mr Sotloff, 31, who was seized in Syria last year, also appeared in that footage with a warning that he would be next.
The British hostage appears at the end of the latest video, released on Tuesday and entitled A Second Message To America. The US has confirmed the video is authentic.
US President Barack Obama said his country would not be “intimidated” by IS, adding: “Their horrific acts only unite us as a country and stiffen our resolve.”
Mr Cameron told the House of Commons: “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.
“It will have the opposite effect. We will be more forthright in the defence of the values, liberty under the rule of law, freedom, democracy that we hold dear.”
He said Britain would continue with its policy of not paying ransoms – which is also the US policy – as such payments funded the promotion of terrorism.
Mr Cameron said diplomatic efforts would be made to make sure other G8 countries do not make ransom payments for hostages.
The UN would be vital in building an effective alliance against IS, he added, saying that the extremist group “needs to be squeezed out of existence”.
Labour leader Ed Miliband said he agreed with Mr Cameron. “Events like this must strengthen, not weaken, our resolve to defeat them and he can be assured of our full support in standing firm against them,” he said.
BBC assistant political editor Norman Smith said Mr Cameron had used “deliberately defiant language” that could hint at the possibility of military action.
He said: “In terms of specifics, not much, although I do think the prime minister was perhaps suggesting that Britain would be prepared to look at joining in with other countries, particularly in the region, and consider air strikes.
“He wasn’t explicit about that – but you sense that might be a direction of travel.”
Foreign Secretary Philip Hammond earlier said the UK will look at “every possible option” to protect the British hostage.
He said the UK government had been aware of a British citizen being held by IS for “some time”.
Speaking after a meeting of the Cobra emergency committee, Mr Hammond said: “I can assure you we will look at every possible option to protect this person.”
He said the release of the latest video would not make any difference to the government’s overall strategy.
“We have to deal with IS on the basis of the wider threat that they pose to the British public as well as this individual.
“If we judge that air strikes could be beneficial, could be the best way to do that, then we will certainly consider them but we have made no decision to do so at the moment.”
By Nick Robinson, BBC political editor
Both Tory and Lib Dem ministers tell me that they see both a moral and a legal case for air strikes in Iraq provided they are requested by the Iraqi government and/or the Kurdish Peshmerga, are backed by a wide number of countries and have a clear military objective.
Syria, they say, is different as they are not prepared to act with President Assad who, in any case, has a fierce air defence system which could threaten coalition jets.
On Wednesday morning the former Labour Foreign Secretary Jack Straw added his voice to those on the Labour benches backing strikes. Peter Hain and John Woodcock – who was an adviser to former Defence Secretary Geoff Hoon – have already said so.
Will David Cameron escape from underneath what friends of his describe as the black cloud of British involvement in Iraq?
Ed Miliband backed action in Libya but blocked it in Syria. What will he do now?
The US has launched more than 120 air strikes in Iraq in the past month, in an attempt to help Kurdish forces curb the advance of IS militants.
The extreme Sunni group has seized large swathes of territory in Iraq and Syria in recent months, declaring a new caliphate, or Islamic state.
Britain has not taken military action against IS so far, but Mr Cameron refused to rule out the possibility earlier this week.
Former Foreign Secretary Jack Straw said his “instinct” was for the UK to join US air strikes in Iraq.
“We should learn from the past, but not be paralysed by it,” Mr Straw told BBC Radio 4’s Today Programme, referring to the previous conflict in Iraq.
But Conservative MP Mark Field, who sits on the intelligence and security committee, said air strikes were “not the answer” and that further diplomatic work was needed.
“We have got to be patient,” he said. “This is not something that is going to be turned around in a matter of weeks or months.”
Home Secretary Theresa May called Islamic State a “group of murderous psychopaths”.
She also said the government would continue to take steps to have the powers that would protect national security.
The Muslim Council of Britain also condemned Mr Sotloff’s murder.
Secretary general Dr Shuja Shafi said: “This depraved act is yet another illustration of how this group betrays the very principles of Islam they claim to uphold.”
On Monday the prime minister outlined plans for new powers to seize terrorist suspects’ passports and stop British-born extremists from returning to the UK.