The woman was identified as Kayla Jean Mueller, an American who went to Syria to do aid work, but there was no independent verification of the militants' claim. The statement appeared on a militant website commonly used by the group and was also distributed by ISIS-affiliated Twitter users.

The 26-year-old Mueller, of Prescott, Arizona, is the only known remaining U.S. hostage held by the ISIS group.

If the death is confirmed, she would be the fourth American to die while being held by ISIS militants. Three other Americans - journalists James Foley and Steven Sotloff, and aid worker Peter Kassig - were beheaded by the group.

Journalist Austin Tice, of Houston, Texas, disappeared in August 2012 while covering Syria's war. It's not clear what entity is holding him, but it is not believed to be the ISIS group or the Syrian government, his family has said.

The announcement was the second time this week that extremists announced the death of a hostage. They released a video Tuesday showing Jordanian air force Lt. Muath al-Kaseasbeh, also 26, being burned to death in a cage in gruesome images that caused outrage in Jordan and the rest of the region.

Mueller's parents said in a statement addressed to ISIS group leaders Friday that the claim of their daughter's death concerned them but they were still hopeful she was alive.

Al-Kaseasbeh, whose F-16 came down in December while conducting airstrikes as part of a campaign against the militants by a U.S.-led coalition, was believed to have been killed in early January.

Friday's statement said Mueller was killed in the militants' stronghold of Raqqa in northern Syria during Muslim prayers - which usually take place around midday - in airstrikes that targeted "the same location for more than an hour."

It published photos purportedly of the bombed site, showing a severely damaged three-story building, but offered no proof or images of Mueller.

ISIS Shows targeted position

The statement said no ISIS militants were killed in the airstrikes, raising further questions about the veracity of the claim.

Jordanian government spokesman Mohammed al-Momani said it was investigating.

"It's part of their 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," he added.

A Raqqa-based collective of anti-IS activists known as "Raqqa is Being Slaughtered Silently" said the planes targeted multiple ISIS positions and headquarters in the western and eastern countryside of Raqqa, sending up columns of smoke. Explosions could be heard in the city. The collective said there were no recorded civilian casualties, and did not mention any IS casualties.

The Britain-based Syrian Observatory for Human Rights said dozens of ISIS members were killed in coalition airstrikes that targeted a tank and vehicle depot in the area of al-Madajen and at least six other ISIS positions, including a training camp and a prison.

American officials said they also were looking into the report.

Bernadette Meehan, the spokeswoman for President Barack Obama's National Security Council, said the White House has "not at this time seen any evidence that corroborates" the claim."

"We are obviously deeply concerned by these reports," she added.

A U.S. official said coalition aircraft did conduct bombing near Raqqa on Friday, but had nothing to confirm the claim that the American captive was killed in the airstrike. He spoke on condition of anonymity because he wasn't authorized to discuss the issue with reporters.

A bomb with Koranic verses is pictured on a Royal Jordanian Air Force plane at an air base before it's launch to strike the Islamic state in the Syrian city of Raqqa February 5, 2015. (Reuters/Petra News Agency)

White House spokesman Eric Schultz told reporters the U.S. coordinates with the Jordanian air force as they fly airstrikes. He wouldn't say whether the U.S. was aware of the hostage's location.

Mueller had been working in Turkey assisting Syrian refugees, according to a 2013 article in The Daily Courier, her hometown newspaper. She told the paper that she was drawn to help with the situation in Syria.

"For as long as I live, I will not let this suffering be normal," she said. "It's important to stop and realize what we have, why we have it and how privileged we are. And from that place, start caring and get a lot done."

According to the newspaper, Mueller had been working with the humanitarian aid agency Support to Life, as well as a local organization that helped female Syrian refugees develop skills.

On Sunday, Obama said the U.S. was "deploying all the assets that we can" to find Mueller.

"We are in very close contact with the family trying to keep them updated," he said in an interview with NBC's "Today" show. "Obviously this is something that is heart-breaking for the family, and we want to make sure we do anything we can to make sure that any American citizen is rescued from this situation."

Mueller's identity had not been disclosed until now out of fears for her safety.

Jordan has stepped up its attacks against the ISIS group after the extremists announced they had put al-Kasaesbeh to death.

The Syrian government said Thursday that dozens of Jordanian fighter jets had bombed ISIS training centers and weapons storage sites. It did not say where the attacks occurred.

The Jordanian military said its warplanes carried out a series of attacks Friday and "destroyed the targets and returned safely." It did not elaborate.

Activists who monitor the Syrian conflict from inside the country said coalition planes hit several targets on the edges and outskirts of Raqqa in quick succession.