"We do not pay ransoms," the US State Department said after it emerged journalist James Foley's captors demanded a ransom of €100 million (£80 million) before his death.
"One of the main ways Isil has been funded throughout this conflict has been from ransom payments that others have paid," spokeswoman Marie Harf said.
"We believe that paying ransoms or making concessions would both put all Americans overseas at greater risk for kidnapping and in harms way, but that ransoms would also fund and finance exactly the groups we are trying to degrade their capabilities," she told reporters.
A British family have told ITV News of their devastation after discovering a close relative is fighting with the Islamic State in Iraq.
A French journalist who was held hostage with James Foley in Syria has told ITV News it was "devastating" to see his murder.