Hours after confirming the death of a US hostage snatched in Syria, President Barack Obama described the anguish of dealing with distraught families, but insisted his government would still not pay ransoms.

Telling loved ones he would not allow ransom payments in return for freedom is "as tough as anything I do," Obama told BuzzFeed in an interview following the death of 26-year-old Kayla Mueller.

The Arizona aid worker was seized in August 2013 in Aleppo.

Last week the Islamic State group claimed she had been killed in a Jordanian air strike in the Syrian city of Raqa, an account the White House has scotched.

Obama said his "immediate reaction was heartbreak" when learning of her death.

But the White House has come under pressure to review its policy of not paying for the freedom of its citizens. Some European hostages whose governments do pay ransoms have been freed.

The policy is in place, he said, because "once we start doing that, not only are we financing their slaughter of innocent people and strengthening their organization, but we're actually making Americans even greater targets for future kidnappings."

Obama said the US had acted in other ways to win Mueller's release, including conducting a special operations raid in Syria.

"We devoted enormous resources and always devote enormous resources to freeing captives or hostages anywhere in the world," he added.

"I deployed an entire operation -- at significant risk -- to rescue not only her but the other individuals who had been held, and probably missed them by a day or two, precisely because we had that commitment."