President Barack Obama said the beheading of a U.S. journalist by Islamic radicals won't deter him from a bombing campaign aimed at driving them back.

"The United State of America will continue to do what we must do to protect our people," he said. "We will be vigilant, and we will be relentless."

Obama spoke a day after the Islamic State militants posted a video on the Internet showing the beheading of journalist James Foley. The White House on wednesday said the video is authentic, and the president called Foley's parents to offer condolences.

The video shows Foley reading a statement that blames Obama for airstrikes on Islamic State militants in Iraq. At the end, he is beheaded. A second man, identified as Steven Sotloff, is shown.

"The life of this American citizen, Obama, depends on your next decision," the black-masked militant in the video says, with a British accent.

Obama made no mention of Sotloff.

"Jim Foley's life stands in stark contrast to these killers," Obama said. "No God would stand for" what the terrorists did, he said, and their claim to be religious was belied by their slaughter of fellow Muslims.

The president authorized U.S. airstrikes on Islamic State fighters earlier this month as the militants pressed their advance across Iraqi territory. Obama said he was acting to protect American military and diplomatic personnel in the northern Iraqi city of Erbil and to break a siege that had trapped thousands of Yezidi civilians on a mountaintop.

He said this week the U.S. would keep up "limited" airstrikes against Islamic State positions, after the bombing stopped the radicals' advance on Erbil and helped Iraqi and Kurdish forces recapture a key dam at Mosul.