The killing of US aid worker Peter Kassig has sparked global horror, with President Barack Obama condemning his beheading by the Islamic State jihadist group as "an act of pure evil".

Kassig's family said it was "heartbroken" by the killing, claimed by IS in a gruesome video that also showed the simultaneous beheadings of at least 18 men described as Syrian military personnel.

It was the latest in a series of atrocities by IS, a Sunni Muslim extremist group that has seized control of large parts of Iraq and Syria.

Kassig, who took the name Abdul-Rahman after converting to Islam, was captured last year and was the fifth Western hostage beheaded by IS after two US reporters and two British aid workers.

"Abdul-Rahman was taken from us in an act of pure evil by a terrorist group that the world rightly associates with inhumanity," Obama said in a statement.

In the undated video released on Sunday, a man who appears to be the same British-accented jihadist who beheaded previous Western hostages stands above a severed head.

"This is Peter Edward Kassig, a US citizen," the black-clad masked executioner says, urging Obama to send more troops back to the region to confront IS.

"Here we are burying the first American crusader in Dabiq, eagerly waiting for the remainder of your armies to arrive," the militant says, referring to a northern Syrian town.

Washington is preparing to double its military personnel in Iraq to up to 3,100 as part of the international campaign it is leading against the jihadists.

European countries including Britain and France have joined the United States in carrying out air strikes against IS in Iraq, and the European Union said Monday that it was "fully committed" to tackling the threat posed by the jihadists.

Flags lowered in mourning

EU foreign policy chief Federica Mogherini and humanitarian aid commissioner Christos Stylianides said the killing of Kassig and the Syrian military personnel showed IS's "resolve to pursue its terror agenda in breach of all universally recognised values and rights".

"All perpetrators of human rights abuses must be held accountable. The EU will spare no effort towards this objective," they said in a statement.

Kassig, an Iraq war veteran, had risked his life to provide medical treatment and relief supplies to those suffering from Syria's civil war.

He founded a group through which he trained some 150 civilians to provide medical aid to people in Syria. His group also gave food, cooking supplies, clothing and medicine to the needy.

Kassig's parents said they were "incredibly proud" of his humanitarian work to help Syrians trapped in a bloody civil war.

"(He) lost his life as a result of his love for the Syrian people and his desire to ease their suffering," Ed and Paula Kassig said in a statement posted on Twitter.

Flags were to be lowered at government buildings in Kassig's home state of Indiana on Monday, Governor Mike Pence said in a statement, calling the killing "an unspeakable act of barbarism".

"Abdul-Rahman Kassig was one of us and he was the best of us. He was... admired by all as a loving son, a dedicated student, an Army Ranger, and a compassionate humanitarian who risked his life to render medical aid to refugees in Syria and Lebanon," Pence said.

During a trip to refugee camps outside the Lebanese capital Beirut in March 2012, Kassig said he found a "shortage of everything except suffering".

"Here, in this land, I have found my calling," Kassig wrote in an email to friends, family and teachers at the time.

"I do not know much, every day that I am here I have more questions and less answers, but what I do know is that I have a chance to do something here, to take a stand. To make a difference."

'They are animals'

US Secretary of State John Kerry said that American government officials had worked alongside Kassig's family to try to secure his release.

"During his time in captivity, his family, and the entire government... worked to avoid this tragic outcome," the top US diplomat said.

British Prime Minister David Cameron said he was "horrified" by the "cold-blooded murder," which French President Francois Hollande called a "crime against humanity".

Burhan Mousa Agha, a Syrian friend who worked with Kassig in Lebanon, described him as a funny, dedicated and brave man.