A video released October 3 purports to show an Islamic State (IS) fighter beheading British hostage Alan Henning.
Henning, 47, a taxi driver and aid volunteer, had joined an aid convoy and was taken captive on December 26, shortly after crossing the border between Turkey and Syria.
The UN Security Council "strongly condemned the heinous and cowardly murder."
British Prime Minister David Cameron on October 4 described Henning's brutal murder as "abhorrent, senseless, and completely unforgivable."
Cameron vowed that Britain will do all it can to find the killers.
President Barack Obama said in a statement that the United States strongly condemns Henning's "brutal murder."
Obama said that Henning worked to improve the lives of the Syrian people and his death is a loss for them, as well as his family and Britain.
Obama says the United States, along with Britain and other allies, will work to bring those responsible for Henning's death to justice.
Earlier on October 3, Obama's top counterterrorism adviser, Lisa Monaco, said, "This is yet again another clear example of the brutality of this group and why the president has articulated and [is] moving out in a comprehensive way to degrade and destroy ISIL."
French President Francois Hollande has also expressed outrage over the murder, pledging to help bring the perpetrators to justice.
The video, which resembled other beheading videos shot by the IS group, ended with an IS masked militant threatening a man they identified as an American, Peter Kassig.
The militant said, "Obama, you have started your aerial bombard of Shams (Syria), which keep on striking our people, so it is only right that we strike the next of your people."
The National Security Council, which advises the U.S. president, said it was using all means to bring home Kassig, a former Army Ranger.
His family said that after leaving the army, Kassig became an aid volunteer.
The video's authenticity could not be immediately identified, though it was released in the same manner as other Islamic State group videos.
IS has previously released videos showing the beheadings of two U.S. journalists -- James Foley and Steven Sotloff -- and British citizen David Haines.
Other foreigners are believed held by the IS. On October 3, the father of John Cantlie, a British photojournalist held by the group, appealed for his release in a video, saying he was a friend of Syria.
Henning's apparent murder came as IS militants besieged the Syrian town of Kobani on the Turkish border.
The outnumbered Kurdish defenders came under fire from IS fighters who have closed in on Kobani despite U.S.-led air strikes against them.
The Syrian Observatory for Human Rights, a British-based monitoring group, said at least 60 mortar rounds were launched against Kurdish positions in the city.
The observatory said a Chechen IS fighter was leading the assault on the strategic town.
Kobani's capture by IS fighters would provide a direct link between areas under their control in Syria's Aleppo and their stronghold in Raqqa to the east.
The fierce fighting came a day after the Turkish government won authorization from parliament to take military action in Syria and Iraq.
Syria's President Bashar al-Assad warned that the Turkish move "represents a real aggression against a member state of the United Nations."
The Pentagon, meanwhile, said aircraft from Saudi Arabia and the United Arab Emirates joined U.S. fighter jets in new bombing raids on October 3.
It said coalition planes hit IS tanks, oil refineries, and a training camp.
American aircraft also conducted three air raids in Iraq, including two northeast of Fallujah.
Dutch Defense Minister Jeanine Hennis-Plasschaert said her country could send F-16 fighter bombers into action over Iraq by this weekend, a move welcomed by the White House.
Australia also decided to join air strikes in Iraq, and Canada's parliament is expected to vote on October 6 to back a plan to send fighter jets.
With reporting by Reuters, AP, and the BBC
