He added: "This underlines the deplorable depths to which these terrorists are prepared to go - savagely murdering a compassionate man.
In Washington, Mr Obama's National Security Council said US intelligence agencies were working to confirm the authenticity of the video. Officials said they were "increasingly convinced" it was genuine.
A spokeswoman said: "If confirmed, we are appalled by the brutal murder of an innocent American aid worker and we express our deepest condolences to his family and friends."
The killing showed the West may have to "think the unthinkable" and commit ground troops to help Iraqi forces beat back the militants from northern Iraq, Lord Dannatt, former head of the Army said.
The 15-minute-long film was released hours after unconfirmed reports Jihadi John, who is now one of the world's most wanted men, had been wounded last week in a US air strike. It was not immediately clear when it was filmed.
The militant, who speaks in a London accent, says: "To Obama, the dog of Rome. Today we are slaughtering the soldiers of Bashar and tomorrow we will be slaughtering your soldiers and with Allah's permission we will break this final and last crusade and the Islamic State will soon, like your puppet David Cameron said, begin to slaughter your people on your streets."
The video then shows the execution of at least 18 pilots and officers from Bashar al Assad's government forces. Later the militant can be seen with a decapitated head at his feet, which he says belongs to Mr Kassig. Mr Kassig makes no propaganda statement in the video, in contrast to the executions in earlier hostage films, and one close friend said he believed he had defied his captors to the end.
Michael Downey, one of Mr Kassig's best friends from Beirut, said: "I think he refused. He was a man of principle and wouldn't give into intimidation from thugs. He never took the easy route."
Mr Cameron earlier this year warned that Britain faces the "greatest and deepest" terror threat in the country's history and the risk posed by Isil, also known as Isis, will last for "decades".
Lord Dannatt, former Chief of the General Staff, called for a national debate in Britain about what action should be taken against the militants.
Western leaders may now have to "think the unthinkable" and send in troops if the combination of air strikes and local forces was unable to counter menace for the jihadists.
He told Sky News more had to be done to attack Isil from the air and by backing Iraqi and Kurdish troops fighting on the ground.
"If that is not enough then we might have to think the unthinkable and possibly engage Western forces on the ground. I don't see that happening in a great rush, there's no appetite for it, there's no political appetite for it.
He went on: "The evidence is showing us that this is not going to go away and that more action is going to have to be taken.
"I don't want to see British troops involved. We have had 10, 12 years of exhaustive intervention in Iraq and Afghanistan.
"But are we just going to wish this away or are we going to take action? That's what has got to be addressed in a national debate."
Sir John Major, the Prime Minister during the 1991 Gulf War, warned Arab nations should play the leading role, or Western involvement would again be portrayed as a crusade.
He said: "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."
The threats to the West followed a strategic shift in the movement, which has previously focused on building up a state ruled by Sharia law in Eastern Syria and northern Iraq, said one analyst.
Prof Peter Neumann of King's College Centre for Study of Radicalisation and Political Violence, said he now expected to see more attacks such as the shooting of a soldier who had been guarding Canada's national war memorial in Ottawa.
He said: "Three weeks ago their spokesman came out with a statement saying attack them wherever you find them. Before they had said come to the Islamic State, we are building the Caliphate, if you agree with us, and you are like minded, then you should come to us."
But the release of the video was interpreted as a sign Isil is shaken by the US-led air strike campaign and reports that it's leader, Abu Bakr al-Baghdadi, had been badly hurt.
Prof Neumann said: "I think the Islamic state is under pressure. They are not expanding any more and that must be frustrating for them because their whole unique selling point is that they deliver, they are the only ones who are unstoppable, but they have been stopped."
Isil is now believed to have just two Western hostages left in captivity, the British journalist John Cantlie and a female American aid worker.
Fawaz Gerges, professor of Middle East politics at the London School of Economics, said: "Hostages are the only means that Isis has to retaliate against the Americans and Europeans. It's really them leveraging their most important weapons. They are hurting, they are bleeding.
He said the video was in response to reports that Al Baghdadi and Jihadi John had been wounded in US air strikes.
He said: "They are over extended, the Iraqi army and its allies are standing up. Major progress has been achieved in Iraq."
