The footage released last night appears to show the beheading of Steven Sotloff, who wrote for the magazine Time.
It has yet to be verified, but the British-born Jihadist who carries out the killing then goes onto threaten a British hostage with death.
That man is understood to have been educated in Scotland and had been an aid worker based on the Turkish border of Syria working with victims of the conflict.
The latest threats from the Islamic State militants follows last month's killing of James Foley, also from America.
David Cameron said the killing was "an absolutely disgusting and despicable act."
The Prime Minister will tomorrow morning chair a meeting of the Government's emergency committee, Cobra.
Labour leader Ed Miliband said: "The killing by (IS) of another hostage and the threat of more violence demonstrates again their murderous barbarism. Their cold-blooded brutality against the innocent offends the values of people throughout the world, wherever they live.
"Their cold-blooded brutality against the innocent offends the values of people throughout the world, wherever they live.
"This shows, as we have recently said, that they are a threat which cannot be ignored.
"Our thoughts are with the families of the victims."
A Foreign Office spokesman said it was urgently investigating the reports of a threat to another hostage, and attempting to verify the tape.
A spokesman for Mr Sotloff's family said they "know of this horrific tragedy and are grieving privately".
The journalist was seized in Syria in August 2013 and had not been seen until he appeared in the video of Mr Foley's killing released by IS last month.
Last week Mr Sotloff's mother Shirley made an emotional video plea for the IS extremists to be "merciful" and spare her son.
In the chilling footage, Mr Sotloff - a freelancer for Time magazine among other publications - is pictured in a Guantanamo Bay-style orange jump suit against a desert backdrop.
He reads out a purported "message to America" in which he tells US president Barack Obama: "I am paying the price of your interference with my life ...
"You've spent billions of pounds US taxpayers' dollars and we have lost thousands of our troops in our previous fighting against the Islamic State, so where is the people's interest in reigniting this war?"
The jihadist, believed to be a Briton nicknamed "John" by captives, says: "I am back, Obama, and I am back because of your arrogant foreign policy towards the Islamic State, because of your insistence on continuing your bombings and ... on Mosul Dam, despite our serious warnings.
"Just as your missiles continue to strike our people, our knife will continue to strike the necks of your people."
Dressed in black and wielding a short knife, the extremist also warns other governments against entering "this evil alliance of America against the Islamic State".
The video, which ends with another hostage said to be British being threatened, has surfaced in the week that world leaders are due to gather in Wales for a Nato summit.
Giving his reaction after addressing a meeting of Tory MPs and peers in Parliament this evening, Mr Cameron said: "It is an absolutely disgusting and despicable act.
"I will be making a statement later."
A Foreign Office spokesman said: "We are aware of a video which purports to be the murder of a US national and includes a threat to another hostage. We are urgently working to verify the authenticity of the video."
White House spokesman Josh Earnest said they had been in touch with the latest US victim's family and they were attempting to verify the footage.
He said: "This is something that the administration has been watching very carefully since this threat against his life was made a few weeks ago.
"Our thoughts and prayers first and foremost are with Mr. Sotloff's family, and those who worked with him. The United States has dedicated significant time and resources to trying to rescue Mr Sotloff."
Yesterday Mr Cameron announced a package of measures to combat the danger from British jihadists returning from fighting in Syria and Iraq to carry out attacks here.
He said police would be given powers to confiscate passports at airports, and suggested that suspected extremists could be barred from re-entering the country even if they are UK nationals.