"The United States strongly condemns the barbaric murder of UK citizen David Haines by the terrorist group ISIL," Obama said in a statement, using an alternate acronym for the group.
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve."
The latest two-minute-27-second video, which shows Haines being killed by a masked militant, is titled "A Message to the Allies of America."
The executioner, who speaks in English with an apparently British accent, blames Prime Minister David Cameron for joining forces with the United States, which has said it is at "war" with the jihadists and launched air strikes against them in Iraq.
"Our hearts go out to the family of Mr Haines and to the people of the United Kingdom," Obama said, vowing to hunt down the killers and destroy IS.
"We will work with the United Kingdom and a broad coalition of nations from the region and around the world to bring the perpetrators of this outrageous act to justice, and to degrade and destroy this threat to the people of our countries, the region and the world," he said.
US Secretary of State John Kerry is currently traveling to meet with US allies, hoping to forge a broad international coalition against IS in Iraq and Syria, that will include Arab nations, European nations, and others.
Scottish-born Haines, 44, was taken hostage in Syria in March 2013 and was threatened in a video released this month depicting an IS militant beheading US journalist Steven Sotloff.
