In a joint opinion piece published Thursday in The Times of London newspaper to mark the beginning of the NATO summit in Wales, the two leaders warned that democratic nations could not afford to be intimidated by the threat of terrorists.
"If terrorists think we will weaken in the face of their threats they could not be more wrong. Countries like the UK and the US will not be cowed by barbaric killers," the two leaders wrote.
Their remarks came after Tuesday's murder of American journalist Stephen Sotloff, held by the IS in Iraq, and fellow US journalist James Foley two weeks ago.
The extremists have also threatened to kill a British hostage in revenge for the British military presence in Iraq to combat the group's growing aggression.