A British Muslim leader condemned the latest killing. Shaukat Warraich, editor of Imamsonline.com, said: 'The murder of Abdul-Rahman Kassig is an affront to Islam. The murderous criminals are a stain on humanity and their wicked ways must be stopped.
'To take the life of another, one whose life has been dedicated to providing aid to our brothers and sisters suffering in Syria, Iraq and the surrounding regions further highlights the inhumane, revolting and unIslamic terrorists for what they really are.'
Labour leader Ed Miliband said: 'My deepest sympathies go to the family of Abdul-Rahman Kassig today. These brutal killers must face justice.
'I am sickened by the senseless murder of a man who had dedicated his life to helping others.'
Former prime minister Sir John Major described the murder as '13th-century barbarism'.
He told BBC1's The Andrew Marr Show: 'The people they are murdering, which makes it doubly worse, triply worse, are people who actually went there to help those in difficulty and in need.
'They are being murdered in the most brutal ways, almost beyond belief.'
On whether Britain is in a position to do something about the situation, Sir John added: 'I don't think we can do all that much about it alone, but can we contribute to helping other people to do something about it - I think the answer is undoubtedly yes.
'Though unless we want the old argument that the crusaders have come in to attack, we really need to support other Arabs on the ground and use our power in other ways to help them - surveillance, training, provide weapons and so forth - I think that is a proper role for us.'
Shadow foreign secretary Douglas Alexander said: 'If this video is authenticated, all of us in the UK will feel revulsion at this latest sickening murder. It only emphasises the scale of the threat posed by Isil and the importance of the international community working together to confront that threat.'
The militant Islamic State group has beheaded and shot dead hundreds of captives - mainly Syrian and Iraqi soldiers - during its sweep across the two countries, and has celebrated mass killings in a series of slickly produced but extremely graphic videos.
The group has declared an Islamic caliphate in the areas under its control in Syria and Iraq, which it governs according to a harsh version of Shariah law.
The U.S. began launching air strikes in Iraq and Syria earlier this year in a bid to halt the group's rapid advance and eventually degrade and destroy it.