As US jets continued to strike jihadist targets despite a threat to kill a second reporter, Obama said: "When people harm Americans anywhere, we do what's necessary to see that justice is done."
Shortly after he spoke, the State Department asked for 300 more US troops to be sent to Iraq to protect US facilities.
Obama was speaking after the so-called "Islamic State," which has seized much of eastern Syria and northern Iraq, released a video showing a masked militant beheading US reporter James Foley.
The black-clad man said the 40-year-old freelance journalist, who was kidnapped in northern Syria in November 2012, had been killed to avenge American air strikes against his movement.
He paraded a second US reporter, Steven Sotloff, before the camera and said he too would die unless Obama changes course.
Obama did not directly refer to Sotloff in his brief address -- and the Pentagon confirmed that airstrikes would continue -- but he paid tribute to Foley and said the Islamic State must be defeated.
"Jim Foley's life stands in stark contrast to his killers," he said, branding the militants genocidal murderers who target civilians and subject women and children to "torture and rape and slavery."
"Their victims are overwhelmingly Muslim and no faith teaches people to massacre innocents," he said, dismissing the IS claim to represent the aspirations of a global Muslim caliphate.
"No just God would stand for what they did yesterday and what they do every single day," he declared.
"We will be vigilant and we will be relentless... From governments and peoples across the Middle East, there has to be a common effort to extract this cancer so it does not spread."
US intelligence believes the video is genuine, and the British government held a crisis meeting to launch an investigation because Foley's executioner spoke English with a London accent.
"We have not identified the individual responsible, but from what we have seen, it looks increasingly likely that it is a British citizen." Prime Minister David Cameron told reporters. "This is deeply shocking."
- 'A war crime' -
Foley's parents, John and Diane, appeared on the lawn of their home in New Hampshire to pay tribute to their son -- the oldest of five adult children -- and call for other hostages to be released.
"Jim would never want us to hate or be bitter. We cannot do that and we are just so very proud of Jimmy and we are praying for the strength to love like he did," Diane said.
US Central Command said 14 air strikes had been carried out on IS targets in Iraq in the 24 hours since the video was released.
The United Nations and Europe's top powers condemned the killing, and France warned the world faces the "most serious international situation" since 2001, the year of the September 11 attacks.
In a significant shift from its usual policy, Germany said it was ready to send weapons to support Iraqi Kurds against IS, while France vowed to hold a conference on regional security.
Foley was an experienced correspondent who had covered wars in Afghanistan and Libya before heading to Syria, contributing reports to GlobalPost, Agence France-Presse and other outlets.
AFP chairman Emmanuel Hoog described Foley "as a brave, independent and impartial journalist" whose work in Syria and other war zones was widely admired.
According to witnesses, Foley was seized in the northern Syrian province of Idlib on November 22, 2012.
- 'A message to America' -
In the nearly five-minute video, Foley is seen kneeling on the ground, dressed in an orange outfit that resembles those worn by prisoners held at the US naval base at Guantanamo Bay.
"Any aggression toward the Islamic State is an aggression toward Muslims from all walks of life who have accepted the Islamic caliphate as their leadership," the masked militant declares.
In June, the group then known as the Islamic State in Iraq and the Levant declared the dawn of a Muslim caliphate and seized control of a swath of eastern Syria and northern Iraq.
This month, Obama reacted by ordering US warplanes to counter threats to US personnel in the Kurdish regional capital Arbil or to civilian refugees from Iraqi religious minority groups.
He has insisted the scope of the strikes would remain limited but Iraqi officials and observers have argued only foreign intervention could turn the tide on jihadist expansion in Iraq.
According to Kurdish officers, a US air strike carried out early Wednesday targeted an apparent jihadist meeting at a school in the area of the dam.
- Iraq offensive stalled -
Shiite militias, federal soldiers, Kurdish troops and Sunni Arab tribes have been battling IS for weeks in some areas but have been unable to clinch a decisive victory.
An offensive launched on Tuesday against former Iraqi dictator Saddam Hussein's hometown Tikrit was presented as a major push to liberate the city, but it appeared to have stalled a few hours later.
While IS was under pressure in Iraq, its forces were advancing in the northern Syrian province of Raqa, assaulting an airbase that is the last government bastion in the region.
In northern Iraq, the UN refugee agency said it has begun a massive 10-day operation to provide assistance to the hundreds of thousands of people displaced by violence.