President Barack Obama and British Prime Minister David Cameron say their countries will not be intimidated by "barbaric killers." Their comments come after Islamic State militants killed two American journalists.
The leaders co-authored an opinion piece in the Times of London newspaper as NATO officials take part in a summit in Britain.
Obama has called for international action to counter Islamic State militants who have taken control of large areas in eastern Syria and northern and western Iraq.
The group has released videos showing the beheading of American journalists James Foley and Steven Sotloff, saying their killings were retaliation for U.S. airstrikes in Iraq targeting the Islamic State.
Obama plans to host a U.N. Security Council session later this month to address the threat posed by foreign fighters like those who have traveled to join terrorist groups in Iraq and Syria.
U.S. Defense Secretary Chuck Hagel said Wednesday that more than 100 U.S. citizens are fighting with the militants in Iraq and Syria, and that the United States and its coalition partners have to do everything possible to stop the Islamic State group now.
Hagel said CNN television that the beheadings of Sotloff and Foley made him sick to his stomach.
The president said Wednesday that those who killed the journalists have failed in whatever they are trying to achieve because the world is "repulsed by their barbarism."
U.S. Vice President Joe Biden said the United States will relentlessly follow the killers of the two Americans "to the gates of hell."
The militant speaking in the Sotloff video threatened the life of British hostage David Cawthorne Haines, who has been described as a security officer for aid agencies.