Barack Obama has vowed that the US will not be intimidated by the beheading of the American journalist Steven Sotloff by Islamic State (Isis) and called for a united international, Arab and Muslim response to its "barbarism".

"We will not be intimidated," the president 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."

The president was speaking in Estonia on the way to a Nato summit in Wales, where the latest bloody twist of the Iraq-Syria crisis is likely to compete with the Ukraine conflict for the attention of leaders.

Obama spoke after the US national security council announced its assessment that the video showing Sotloff's killing was authentic. Many of its features were similar to those of the murder of the journalist James Foley on 19 August.

The UK government held a meeting of its emergency Cobra committee after threats to kill a British hostage who was also shown in the latest video.

The White House, meanwhile, said the president had ordered 350 more troops into Iraq just hours after the release of the video. The new deployment was intended not for "a combat role" but to augment security at the Baghdad embassy and associated "support facilities," it said.

Under fire for his response to the crisis, Obama said the objective of the US was to "ensure that Isil [Islamic State] is not an ongoing threat to the region". The president was criticised last week for saying that the US did not have a "strategy" to deal with the Islamist militant group, which now controls large areas of Syria and Iraq.

But he made clear that the effort needed wide support. "We know that if we are joined by the international community, we can continue to shrink Isil's sphere of influence, its effectiveness, its financing, its military capabilities to the point where it is a manageable problem," Obama said.

"The question is going to be making sure we have the right strategy but also making sure that we have got the international will to do it. What we have got to make sure is that we are organising the Arab world, the Middle East, the Muslim world, along with the international community, to isolate this cancer."

According to the latest Pentagon figures, the US has launched 124 air strikes, including attacks near the Mosul dam on Monday. The strikes were cited by Sotloff's masked and black-clad killer as the reason for the murder.

Obama's appeal for international unity followed widespread condemnation of Sotloff's killing. The British prime minister, David Cameron, condemned the "despicable and barbaric murder" while Ban Ki-moon, the UN secretary-general, said: "I strongly condemn all such despicable crimes and I refuse to accept that whole communities can be threatened by atrocities because of who they are or what they believe."

The French president, François Hollande, said: "This barbaric act, following the assassination of another journalist James Foley, reveals the despicable nature of [Isis]."

But the key question is whether the latest killing will galvanise the US, UK and others into deeper involvement, given that it is now hard to separate the crises in Iraq and Syria.

Washington, London and other capitals have to grapple with the reality that Isis cannot be defeated in Iraq without also tackling its strongholds in Syria, where close to 200,000 people have been killed in the uprising against Bashar al-Assad. Arab countries fear Isis but have so far been reluctant to get involved militarily.

Israeli media, meanwhile, reported that Sotloff, 31, was Jewish and an Israeli citizen who had studied for a degree there. Media had been asked to refrain from reporting this for fear of further increasing the danger to him from his captors.