Their comments come after a video of James Foley’s killing by Islamic State of Iraq and the Levant (ISIS) militants appeared on Tuesday.
ISIS said James Foley’s death was revenge for US air strikes on its fighters in Iraq.
President Barack Obama condemned the killing as “an act of violence that shocks the conscience of the entire world”.
He compared ISIS militants, who control large parts of Syria and Iraq to a “cancer” and said the group’s ideology was “bankrupt”.
The UN, UK and others have also expressed abhorrence at the video.
James Foley’s mother, Diane Foley, said he “gave his life trying to expose the world to the suffering of the Syrian people”.
The Committee to Protect Journalists said it was “extremely concerned for all journalists” still held by ISIS, describing Syria as “the world’s most dangerous place to be a reporter”.
In a statement on Wednesday, the Pentagon said the US had “attempted a rescue operation recently to free a number of American hostages held in Syria”.
It said the operation “involved air and ground components and was focused on a particular captor network within ISIL” (the former name of ISIS).
“Unfortunately, the mission was not successful because the hostages were not present at the targeted location.”
The statement did not specify whether the operation had intended to rescue James Foley, who was kidnapped in Syria in November 2012.
However, senior Obama administration officials – speaking on the condition of anonymity – confirmed this.
They said that several dozen special troops had been dropped by aircraft into Syria in recent weeks to try to rescue US hostages, including James Foley.
They added that the troops had been engaged in a firefight with ISIS militants, killing a number of them. No Americans were killed.
James Foley, 40, had reported extensively across the Middle East, working for GlobalPost and other media outlets including French news agency AFP.
In the ISIS video, titled A Message to America, a man identified as James Foley is dressed in an orange jumpsuit, kneeling in desert-like terrain beside an armed man dressed in black.
He gives a message to his family and links his imminent death to the US government’s bombing campaign of ISIS targets in Iraq.
Clearly under duress, he says: “I call on my friends, family and loved ones to rise up against my real killers, the US government, for what will happen to me is only a result of their complacency and criminality.”
Then the masked militant – who speaks with a British accent – delivers a warning to the US government before killing James Foley: “Any attempt by you, Obama, to deny the Muslims their rights of living in safety under the Islamic caliphate will result in the bloodshed of your people.”
Another captive, identified as American journalist Steven Joel Sotloff, is shown at the end, with the warning that his fate depends on President Barack Obama’s next move.
Steven Joel Sotloff was abducted in northern Syria a year ago.
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