In Jordan, meanwhile, thousands of people marched to demand retribution against IS for murdering a captive pilot.
The jihadists' claim came as Amman said dozens of its jet fighters had struck IS, widening their campaign from Syria to include targets in neighbouring Iraq.
Britain-based monitor the Syrian Observatory for Human Rights said more than 30 IS jihadists were killed in coalition raids Friday around Raqa, the "capital" in Syria of the jihadists' self-proclaimed caliphate.
In a statement on jihadist websites, IS said the woman, whom it named as Kayla Jean Mueller, was buried under rubble after a raid by a Jordanian warplane in Raqa.
"The plane from the crusader coalition bombed a position outside the city of Raqa after Friday prayers," it said.
"No fighter was wounded but we can confirm that an American hostage was killed in the strikes."
The family of aid worker Mueller, 26, urged media restraint in their reporting of the IS claim.
Mueller was captured in August 2013 in Aleppo after leaving a Medecins Sans Frontieres (Doctors Without Borders) hospital, the family statement said.
The family of aid worker Mueller, 26, urged media restraint in their reporting of the IS claim. - AFP Photo
Jordanian Foreign Minister Nasser Judeh denounced the IS claim of her death.
"An old and sick trick used by terrorists and despots for decades: claiming that hostages human shields held captive are killed by air raids," Judeh tweeted.
The IS statement did not show any pictures of a body and there was no independent confirmation of the claim.
The United States said it has not yet seen any proof to confirm the IS claim.
"We are obviously deeply concerned by these reports. We have not at this time seen any evidence that corroborates ISIL's claim," said National Security Council spokeswoman Bernadette Meehan, using another acronym for IS.
'Criminal propaganda'
The US authorities have never given figures on the number of Americans kidnapped in Syria, sticking to a State Department policy of complete silence on any citizens held hostage abroad.
Amman's government spokesman Mohammad al-Momani dismissed the jihadists' claim as "criminal propaganda".
"They have lied that our pilot is alive and tried to negotiate claiming he is alive while they had killed him weeks before," Momani told AFP.
Earlier, thousands of people marched in Amman in solidarity with Maaz al-Kassasbeh, the young Jordanian airman whose burning alive IS showed in a video released this week.
A profile photo of Maaz, the young Jordanian pilot who whose burning alive by IS was shown in a video released last week. - AFP Photo
"We are all Maaz... We are all Jordan," they chanted, some holding placards aloft that read: "Yes to punishment. Yes to the eradication of terrorism."
Queen Rania joined the marchers after weekly prayers at the Al-Husseini mosque, holding a portrait of the pilot with the words "Maaz the martyr of righteousness."
She told the BBC that the battle against IS "is absolutely Jordan's war", but that "to win it we need help from the international community".
Judeh told CNN Jordan would hit the militants with all its might.
"We're going to go after them and we will eradicate them... We are at the forefront. This is our fight," he said.
Jordan has conducted regular air raids against IS across the border in Syria as part of a US-led campaign against the Sunni extremist group.
American F-16 and F-22 jets provided cover for the Jordanian warplanes, with additional support from refuelling tankers and surveillance aircraft, US officials said.
The military said Jordanian warplanes carried out new raids Friday on "selected targets" of the IS group.
Japanese beheaded
On Thursday, King Abdullah II and Queen Rania visited Kassasbeh's family, which has urged the government to "destroy" the jihadists, to pay their condolences.
IS had offered to spare Kassasbeh's life and free Japanese journalist Kenji Goto -- who was later beheaded -- in exchange for Rishawi.
But Jordanian television suggested Kassasbeh was killed on January 3, before IS offered to spare him and free Goto in return for Rishawi's release.
Following the pilot's capture, coalition member the United Arab Emirates withdrew from strike missions over fears for the safety of its pilots, but a US official said in Munich Friday the UAE said flights were likely to resume "in a couple of days".
The world mourns the beheading of Japanese journalist, Kenji Goto who was supposed to be an exchange for Rishawi's release, last week. - AFP Photo
On Thursday, the US military said it was deploying search and rescue planes to northern Iraq in a move designed to shorten the response time needed to reach any pilots who end up in IS-held territory.
Last year, IS seized swathes of territory in Syria and Iraq and declared the caliphate in areas under its control, imposing its brutal interpretation of Islam and committing widespread atrocities.
Jihadists have flocked to Syria since anti-government protests broke out in 2011 and escalated into a multi-sided civil war in which more than 200,000 people have died.
At least 82 people, including 18 children, have been killed by regime bombardment of a rebel-held area near Damascus since Thursday, the Observatory said.
